Daily Papers

Earthquake hazard analysis and design of spatially distributed infrastructure, such as power grids and energy pipeline networks, require scenario-specific ground-motion time histories with realistic frequency content and spatiotemporal coherence. However, producing the large ensembles needed for uncertainty quantification with physics-based simulations is computationally intensive and impractical for engineering workflows. To address this challenge, we introduce Ground-Motion Flow (GMFlow), a physics-inspired latent operator flow matching framework that generates realistic, large-scale regional ground-motion time-histories conditioned on physical parameters. Validated on simulated earthquake scenarios in the San Francisco Bay Area, GMFlow generates spatially coherent ground motion across more than 9 million grid points in seconds, achieving a 10,000-fold speedup over the simulation workflow, which opens a path toward rapid and uncertainty-aware hazard assessment for distributed infrastructure. More broadly, GMFlow advances mesh-agnostic functional generative modeling and could potentially be extended to the synthesis of large-scale spatiotemporal physical fields in diverse scientific domains.

Transformers, the standard implementation for large language models (LLMs), typically consist of tens to hundreds of discrete layers. While more layers can lead to better performance, this approach has been challenged as far from efficient, especially given the superiority of continuous layers demonstrated by diffusion and flow-based models for image generation. We propose the Latent Flow Transformer (LFT), which replaces a block of layers with a single learned transport operator trained via flow matching, offering significant compression while maintaining compatibility with the original architecture. Additionally, we address the limitations of existing flow-based methods in preserving coupling by introducing the Flow Walking (FW) algorithm. On the Pythia-410M model, LFT trained with flow matching compresses 6 of 24 layers and outperforms directly skipping 2 layers (KL Divergence of LM logits at 0.407 vs. 0.529), demonstrating the feasibility of this design. When trained with FW, LFT further distills 12 layers into one while reducing the KL to 0.736 surpassing that from skipping 3 layers (0.932), significantly narrowing the gap between autoregressive and flow-based generation paradigms.

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods still face the challenges of expensive computing and a large number of function evaluations of off-the-shelf solvers in the pixel space. Furthermore, although latent-based generative methods have shown great success in recent years, this particular model type remains underexplored in this area. In this work, we propose to apply flow matching in the latent spaces of pretrained autoencoders, which offers improved computational efficiency and scalability for high-resolution image synthesis. This enables flow-matching training on constrained computational resources while maintaining their quality and flexibility. Additionally, our work stands as a pioneering contribution in the integration of various conditions into flow matching for conditional generation tasks, including label-conditioned image generation, image inpainting, and semantic-to-image generation. Through extensive experiments, our approach demonstrates its effectiveness in both quantitative and qualitative results on various datasets, such as CelebA-HQ, FFHQ, LSUN Church & Bedroom, and ImageNet. We also provide a theoretical control of the Wasserstein-2 distance between the reconstructed latent flow distribution and true data distribution, showing it is upper-bounded by the latent flow matching objective. Our code will be available at https://github.com/VinAIResearch/LFM.git.

This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the underlying distribution. This fixed flow model subsequently regularizes the latent space via an alignment loss, which reformulates the flow matching objective to treat the latents as optimization targets. We formally prove that minimizing this alignment loss establishes a computationally tractable surrogate objective for maximizing a variational lower bound on the log-likelihood of latents under the target distribution. Notably, the proposed method eliminates computationally expensive likelihood evaluations and avoids ODE solving during optimization. As a proof of concept, we demonstrate in a controlled setting that the alignment loss landscape closely approximates the negative log-likelihood of the target distribution. We further validate the effectiveness of our approach through large-scale image generation experiments on ImageNet with diverse target distributions, accompanied by detailed discussions and ablation studies. With both theoretical and empirical validation, our framework paves a new way for latent space alignment.

Unconditional flow-matching trains diffusion models to transport samples from a source distribution to a target distribution by enforcing that the flows between sample pairs are unique. However, in conditional settings (e.g., class-conditioned models), this uniqueness is no longer guaranteed--flows from different conditions may overlap, leading to more ambiguous generations. We introduce Contrastive Flow Matching, an extension to the flow matching objective that explicitly enforces uniqueness across all conditional flows, enhancing condition separation. Our approach adds a contrastive objective that maximizes dissimilarities between predicted flows from arbitrary sample pairs. We validate Contrastive Flow Matching by conducting extensive experiments across varying model architectures on both class-conditioned (ImageNet-1k) and text-to-image (CC3M) benchmarks. Notably, we find that training models with Contrastive Flow Matching (1) improves training speed by a factor of up to 9x, (2) requires up to 5x fewer de-noising steps and (3) lowers FID by up to 8.9 compared to training the same models with flow matching. We release our code at: https://github.com/gstoica27/DeltaFM.git.

Flow matching models have emerged as a powerful method for generative modeling on domains like images or videos, and even on irregular or unstructured data like 3D point clouds or even protein structures. These models are commonly trained in two stages: first, a data compressor is trained, and in a subsequent training stage a flow matching generative model is trained in the latent space of the data compressor. This two-stage paradigm sets obstacles for unifying models across data domains, as hand-crafted compressors architectures are used for different data modalities. To this end, we introduce INRFlow, a domain-agnostic approach to learn flow matching transformers directly in ambient space. Drawing inspiration from INRs, we introduce a conditionally independent point-wise training objective that enables INRFlow to make predictions continuously in coordinate space. Our empirical results demonstrate that INRFlow effectively handles different data modalities such as images, 3D point clouds and protein structure data, achieving strong performance in different domains and outperforming comparable approaches. INRFlow is a promising step towards domain-agnostic flow matching generative models that can be trivially adopted in different data domains.

Detector simulations are an exciting application of modern generative networks. Their sparse high-dimensional data combined with the required precision poses a serious challenge. We show how combining Conditional Flow Matching with transformer elements allows us to simulate the detector phase space reliably. Namely, we use an autoregressive transformer to simulate the energy of each layer, and a vision transformer for the high-dimensional voxel distributions. We show how dimension reduction via latent diffusion allows us to train more efficiently and how diffusion networks can be evaluated faster with bespoke solvers. We showcase our framework, CaloDREAM, on datasets 2 and 3 of the CaloChallenge.

Visual tokenizers play a crucial role in diffusion models. The dimensionality of latent space governs both reconstruction fidelity and the semantic expressiveness of the latent feature. However, a fundamental trade-off is inherent between dimensionality and generation quality, constraining existing methods to low-dimensional latent spaces. Although recent works have leveraged vision foundation models to enrich the semantics of visual tokenizers and accelerate convergence, high-dimensional tokenizers still underperform their low-dimensional counterparts. In this work, we propose RecTok, which overcomes the limitations of high-dimensional visual tokenizers through two key innovations: flow semantic distillation and reconstruction--alignment distillation. Our key insight is to make the forward flow in flow matching semantically rich, which serves as the training space of diffusion transformers, rather than focusing on the latent space as in previous works. Specifically, our method distills the semantic information in VFMs into the forward flow trajectories in flow matching. And we further enhance the semantics by introducing a masked feature reconstruction loss. Our RecTok achieves superior image reconstruction, generation quality, and discriminative performance. It achieves state-of-the-art results on the gFID-50K under both with and without classifier-free guidance settings, while maintaining a semantically rich latent space structure. Furthermore, as the latent dimensionality increases, we observe consistent improvements. Code and model are available at https://shi-qingyu.github.io/rectok.github.io.

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

Flow matching has emerged as a promising framework for training generative models, demonstrating impressive empirical performance while offering relative ease of training compared to diffusion-based models. However, this method still requires numerous function evaluations in the sampling process. To address these limitations, we introduce a self-corrected flow distillation method that effectively integrates consistency models and adversarial training within the flow-matching framework. This work is a pioneer in achieving consistent generation quality in both few-step and one-step sampling. Our extensive experiments validate the effectiveness of our method, yielding superior results both quantitatively and qualitatively on CelebA-HQ and zero-shot benchmarks on the COCO dataset. Our implementation is released at https://github.com/VinAIResearch/SCFlow

Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from straight-line interpolations between prior and target distributions, making generation slower and less accurate due to the need for fine discretization at inference. Recent methods enhance CFM performance by inducing shorter and straighter trajectories but typically rely on computationally expensive mini-batch optimal transport (OT). Drawing insights from entropic optimal transport (EOT), we propose Weighted Conditional Flow Matching (W-CFM), a novel approach that modifies the classical CFM loss by weighting each training pair (x, y) with a Gibbs kernel. We show that this weighting recovers the entropic OT coupling up to some bias in the marginals, and we provide the conditions under which the marginals remain nearly unchanged. Moreover, we establish an equivalence between W-CFM and the minibatch OT method in the large-batch limit, showing how our method overcomes computational and performance bottlenecks linked to batch size. Empirically, we test our method on unconditional generation on various synthetic and real datasets, confirming that W-CFM achieves comparable or superior sample quality, fidelity, and diversity to other alternative baselines while maintaining the computational efficiency of vanilla CFM.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

We introduce a novel generative model for video prediction based on latent flow matching, an efficient alternative to diffusion-based models. In contrast to prior work, we keep the high costs of modeling the past during training and inference at bay by conditioning only on a small random set of past frames at each integration step of the image generation process. Moreover, to enable the generation of high-resolution videos and to speed up the training, we work in the latent space of a pretrained VQGAN. Finally, we propose to approximate the initial condition of the flow ODE with the previous noisy frame. This allows to reduce the number of integration steps and hence, speed up the sampling at inference time. We call our model Random frame conditioned flow Integration for VidEo pRediction, or, in short, RIVER. We show that RIVER achieves superior or on par performance compared to prior work on common video prediction benchmarks, while requiring an order of magnitude fewer computational resources.

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach has not yet led to comparable fidelity. There are several key obstacles: (i) the encoding into a lower-dimensional latent space makes the underlying (forward) mapping non-linear; (ii) the data likelihood term is usually intractable; and (iii) learned generative models struggle to recover rare, atypical data modes during inference. We present FLAIR, a novel training free variational framework that leverages flow-based generative models as a prior for inverse problems. To that end, we introduce a variational objective for flow matching that is agnostic to the type of degradation, and combine it with deterministic trajectory adjustments to recover atypical modes. To enforce exact consistency with the observed data, we decouple the optimization of the data fidelity and regularization terms. Moreover, we introduce a time-dependent calibration scheme in which the strength of the regularization is modulated according to off-line accuracy estimates. Results on standard imaging benchmarks demonstrate that FLAIR consistently outperforms existing diffusion- and flow-based methods in terms of reconstruction quality and sample diversity.

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite their effectiveness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, we propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations. Additionally, we propose a lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost. Extensive experiments on ImageNet 256x256 demonstrate that BFM establishes a substantially improved Pareto frontier over existing Flow Matching methods, achieving 2.1x to 4.9x accelerations in inference complexity at comparable generation performance. Code is available at https://github.com/mlvlab/BFM.

Recently, there has been tremendous progress in visual synthesis and the underlying generative models. Here, diffusion models (DMs) stand out particularly, but lately, flow matching (FM) has also garnered considerable interest. While DMs excel in providing diverse images, they suffer from long training and slow generation. With latent diffusion, these issues are only partially alleviated. Conversely, FM offers faster training and inference but exhibits less diversity in synthesis. We demonstrate that introducing FM between the Diffusion model and the convolutional decoder offers high-resolution image synthesis with reduced computational cost and model size. Diffusion can then efficiently provide the necessary generation diversity. FM compensates for the lower resolution, mapping the small latent space to a high-dimensional one. Subsequently, the convolutional decoder of the LDM maps these latents to high-resolution images. By combining the diversity of DMs, the efficiency of FMs, and the effectiveness of convolutional decoders, we achieve state-of-the-art high-resolution image synthesis at 1024^2 with minimal computational cost. Importantly, our approach is orthogonal to recent approximation and speed-up strategies for the underlying DMs, making it easily integrable into various DM frameworks.

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely on a standard Gaussian distribution, a choice inherited from diffusion models, and rarely consider the source distribution itself as an optimization target in such settings. In this work, we show that principled design of the source distribution is not only feasible but also beneficial at the scale of modern text-to-image systems. Specifically, we propose learning a condition-dependent source distribution under flow matching objective that better exploit rich conditioning signals. We identify key failure modes that arise when directly incorporating conditioning into the source, including distributional collapse and instability, and show that appropriate variance regularization and directional alignment between source and target are critical for stable and effective learning. We further analyze how the choice of target representation space impacts flow matching with structured sources, revealing regimes in which such designs are most effective. Extensive experiments across multiple text-to-image benchmarks demonstrate consistent and robust improvements, including up to a 3x faster convergence in FID, highlighting the practical benefits of a principled source distribution design for conditional flow matching.

Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit unexpected scaling behavior. We argue that this dependence arises from the model's training objective, which poses a denoising task with little incentive to learn semantic representations. We introduce Self-Flow: a self-supervised flow matching paradigm that integrates representation learning within the generative framework. Our key mechanism, Dual-Timestep Scheduling, applies heterogeneous noise levels across tokens, creating an information asymmetry that forces the model to infer missing information from corrupted inputs. This drives learning strong representations alongside generative capabilities without external supervision. Our method generalizes across modalities and enables multi-modal training while following expected scaling laws, achieving superior image, video, and audio generation.

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although inverse problem solving has been extensively explored using diffusion models, it has not been rigorously examined within the broader context of flow models. Therefore, here we extend the diffusion inverse solvers (DIS) - which perform posterior sampling by combining a denoising diffusion prior with an likelihood gradient - into the flow framework. Specifically, by driving the flow-version of Tweedie's formula, we decompose the flow ODE into two components: one for clean image estimation and the other for noise estimation. By integrating the likelihood gradient and stochastic noise into each component, respectively, we demonstrate that posterior sampling for inverse problem solving can be effectively achieved using flows. Our proposed solver, Flow-Driven Posterior Sampling (FlowDPS), can also be seamlessly integrated into a latent flow model with a transformer architecture. Across four linear inverse problems, we confirm that FlowDPS outperforms state-of-the-art alternatives, all without requiring additional training.

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fr\'echet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256times256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that na\"ive linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in O(L) speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.

Generative models have excelled in audio tasks using approaches such as language models, diffusion, and flow matching. However, existing generative approaches for speech enhancement (SE) face notable challenges: language model-based methods suffer from quantization loss, leading to compromised speaker similarity and intelligibility, while diffusion models require complex training and high inference latency. To address these challenges, we propose FlowSE, a flow-matching-based model for SE. Flow matching learns a continuous transformation between noisy and clean speech distributions in a single pass, significantly reducing inference latency while maintaining high-quality reconstruction. Specifically, FlowSE trains on noisy mel spectrograms and optional character sequences, optimizing a conditional flow matching loss with ground-truth mel spectrograms as supervision. It implicitly learns speech's temporal-spectral structure and text-speech alignment. During inference, FlowSE can operate with or without textual information, achieving impressive results in both scenarios, with further improvements when transcripts are available. Extensive experiments demonstrate that FlowSE significantly outperforms state-of-the-art generative methods, establishing a new paradigm for generative-based SE and demonstrating the potential of flow matching to advance the field. Our code, pre-trained checkpoints, and audio samples are available.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into a straight line for a few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of flow matching is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned v-prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, FID = 10.05).

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (epsilon-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers considerably improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Explicitly disentangling style and content in vision models remains challenging due to their semantic overlap and the subjectivity of human perception. Existing methods propose separation through generative or discriminative objectives, but they still face the inherent ambiguity of disentangling intertwined concepts. Instead, we ask: Can we bypass explicit disentanglement by learning to merge style and content invertibly, allowing separation to emerge naturally? We propose SCFlow, a flow-matching framework that learns bidirectional mappings between entangled and disentangled representations. Our approach is built upon three key insights: 1) Training solely to merge style and content, a well-defined task, enables invertible disentanglement without explicit supervision; 2) flow matching bridges on arbitrary distributions, avoiding the restrictive Gaussian priors of diffusion models and normalizing flows; and 3) a synthetic dataset of 510,000 samples (51 styles times 10,000 content samples) was curated to simulate disentanglement through systematic style-content pairing. Beyond controllable generation tasks, we demonstrate that SCFlow generalizes to ImageNet-1k and WikiArt in zero-shot settings and achieves competitive performance, highlighting that disentanglement naturally emerges from the invertible merging process.

Diffusion models can learn rich representations during data generation, showing potential for Self-Supervised Learning (SSL), but they face a trade-off between generative quality and discriminative performance. Their iterative sampling also incurs substantial computational and energy costs, hindering industrial and edge AI applications. To address these issues, we propose the Flow Matching-based Foundation Model (FlowFM), which jointly trains a representation encoder and a conditional flow matching generator. This decoupled design achieves both high-fidelity generation and effective recognition. By using flow matching to learn a simpler velocity field, FlowFM accelerates and stabilizes training, improving its efficiency for representation learning. Experiments on wearable sensor data show FlowFM reduces training time by 50.4\% compared to a diffusion-based approach. On downstream tasks, FlowFM surpassed the state-of-the-art SSL method (SSL-Wearables) on all five datasets while achieving up to a 51.0x inference speedup and maintaining high generative quality. The implementation code is available at https://github.com/Okita-Laboratory/jointOptimizationFlowMatching.

We propose continuous adversarial flow models, a type of continuous-time flow model trained with an adversarial objective. Unlike flow matching, which uses a fixed mean-squared-error criterion, our approach introduces a learned discriminator to guide training. This change in objective induces a different generalized distribution, which empirically produces samples that are better aligned with the target data distribution. Our method is primarily proposed for post-training existing flow-matching models, although it can also train models from scratch. On the ImageNet 256px generation task, our post-training substantially improves the guidance-free FID of latent-space SiT from 8.26 to 3.63 and of pixel-space JiT from 7.17 to 3.57. It also improves guided generation, reducing FID from 2.06 to 1.53 for SiT and from 1.86 to 1.80 for JiT. We further evaluate our approach on text-to-image generation, where it achieves improved results on both the GenEval and DPG benchmarks.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

Diffusion models, and their generalization, flow matching, have had a remarkable impact on the field of media generation. Here, the conventional approach is to learn the complex mapping from a simple source distribution of Gaussian noise to the target media distribution. For cross-modal tasks such as text-to-image generation, this same mapping from noise to image is learnt whilst including a conditioning mechanism in the model. One key and thus far relatively unexplored feature of flow matching is that, unlike Diffusion models, they are not constrained for the source distribution to be noise. Hence, in this paper, we propose a paradigm shift, and ask the question of whether we can instead train flow matching models to learn a direct mapping from the distribution of one modality to the distribution of another, thus obviating the need for both the noise distribution and conditioning mechanism. We present a general and simple framework, CrossFlow, for cross-modal flow matching. We show the importance of applying Variational Encoders to the input data, and introduce a method to enable Classifier-free guidance. Surprisingly, for text-to-image, CrossFlow with a vanilla transformer without cross attention slightly outperforms standard flow matching, and we show that it scales better with training steps and model size, while also allowing for interesting latent arithmetic which results in semantically meaningful edits in the output space. To demonstrate the generalizability of our approach, we also show that CrossFlow is on par with or outperforms the state-of-the-art for various cross-modal / intra-modal mapping tasks, viz. image captioning, depth estimation, and image super-resolution. We hope this paper contributes to accelerating progress in cross-modal media generation.

Generating full-body human gestures based on speech signals remains challenges on quality and speed. Existing approaches model different body regions such as body, legs and hands separately, which fail to capture the spatial interactions between them and result in unnatural and disjointed movements. Additionally, their autoregressive/diffusion-based pipelines show slow generation speed due to dozens of inference steps. To address these two challenges, we propose GestureLSM, a flow-matching-based approach for Co-Speech Gesture Generation with spatial-temporal modeling. Our method i) explicitly model the interaction of tokenized body regions through spatial and temporal attention, for generating coherent full-body gestures. ii) introduce the flow matching to enable more efficient sampling by explicitly modeling the latent velocity space. To overcome the suboptimal performance of flow matching baseline, we propose latent shortcut learning and beta distribution time stamp sampling during training to enhance gesture synthesis quality and accelerate inference. Combining the spatial-temporal modeling and improved flow matching-based framework, GestureLSM achieves state-of-the-art performance on BEAT2 while significantly reducing inference time compared to existing methods, highlighting its potential for enhancing digital humans and embodied agents in real-world applications. Project Page: https://andypinxinliu.github.io/GestureLSM

Taming diffusion models for generative segmentation has attracted increasing attention. While existing approaches primarily focus on architectural tweaks or training heuristics, there remains a limited understanding of the intrinsic mismatch between continuous flow matching objectives and discrete perception tasks. In this work, we revisit diffusion segmentation from the perspective of vector field learning. We identify two key limitations of the commonly used flow matching objective: gradient vanishing and trajectory traversing, which result in slow convergence and poor class separation. To tackle these issues, we propose a principled vector field reshaping strategy that augments the learned velocity field with a detached distance-aware correction term. This correction introduces both attractive and repulsive interactions, enhancing gradient magnitudes near centroids while preserving the original diffusion training framework. Furthermore, we design a computationally efficient, quasi-random category encoding scheme inspired by Kronecker sequences, which integrates seamlessly with an end-to-end pixel neural field framework for pixel-level semantic alignment. Extensive experiments consistently demonstrate significant improvements over vanilla flow matching approaches, substantially narrowing the performance gap between generative segmentation and strong discriminative specialists.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms na\"ive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. We will release our code at https://github.com/CompVis/diff2flow.

In this paper, we study the diffusability (learnability) of variational autoencoders (VAE) in latent diffusion. First, we show that pixel-space diffusion trained with an MSE objective is inherently biased toward learning low and mid spatial frequencies, and that the power-law power spectral density (PSD) of natural images makes this bias perceptually beneficial. Motivated by this result, we propose the Spectrum Matching Hypothesis: latents with superior diffusability should (i) follow a flattened power-law PSD (Encoding Spectrum Matching, ESM) and (ii) preserve frequency-to-frequency semantic correspondence through the decoder (Decoding Spectrum Matching, DSM). In practice, we apply ESM by matching the PSD between images and latents, and DSM via shared spectral masking with frequency-aligned reconstruction. Importantly, Spectrum Matching provides a unified view that clarifies prior observations of over-noisy or over-smoothed latents, and interprets several recent methods as special cases (e.g., VA-VAE, EQ-VAE). Experiments suggest that Spectrum Matching yields superior diffusion generation on CelebA and ImageNet datasets, and outperforms prior approaches. Finally, we extend the spectral view to representation alignment (REPA): we show that the directional spectral energy of the target representation is crucial for REPA, and propose a DoG-based method to further improve the performance of REPA. Our code is available https://github.com/forever208/SpectrumMatching.

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation through approximate SDE solutions, which limit scalability. In this work, we propose SDE Matching, a new simulation-free method for training Latent SDEs. Inspired by modern Score- and Flow Matching algorithms for learning generative dynamics, we extend these ideas to the domain of stochastic dynamics for time series and sequence modeling, eliminating the need for costly numerical simulations. Our results demonstrate that SDE Matching achieves performance comparable to adjoint sensitivity methods while drastically reducing computational complexity.

Dataset distillation seeks to synthesize a highly compact dataset that achieves performance comparable to the original dataset on downstream tasks. For the classification task that use pre-trained self-supervised models as backbones, previous linear gradient matching optimizes synthetic images by encouraging them to mimic the gradient updates induced by real images on the linear classifier. However, this batch-level formulation requires loading thousands of real images and applying multiple rounds of differentiable augmentations to synthetic images at each distillation step, leading to substantial computational and memory overhead. In this paper, we introduce statistical flow matching , a stable and efficient supervised learning framework that optimizes synthetic images by aligning constant statistical flows from target class centers to non-target class centers in the original data. Our approach loads raw statistics only once and performs a single augmentation pass on the synthetic data, achieving performance comparable to or better than the state-of-the-art methods with 10x lower GPU memory usage and 4x shorter runtime. Furthermore, we propose a classifier inheritance strategy that reuses the classifier trained on the original dataset for inference, requiring only an extremely lightweight linear projector and marginal storage while achieving substantial performance gains.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Flow matching models have recently emerged as an efficient alternative to diffusion, especially for text-guided image generation and editing, offering faster inference through continuous-time dynamics. However, existing flow-based editors predominantly support global or single-instruction edits and struggle with multi-instance scenarios, where multiple parts of a reference input must be edited independently without semantic interference. We identify this limitation as a consequence of globally conditioned velocity fields and joint attention mechanisms, which entangle concurrent edits. To address this issue, we introduce Instance-Disentangled Attention, a mechanism that partitions joint attention operations, enforcing binding between instance-specific textual instructions and spatial regions during velocity field estimation. We evaluate our approach on both natural image editing and a newly introduced benchmark of text-dense infographics with region-level editing instructions. Experimental results demonstrate that our approach promotes edit disentanglement and locality while preserving global output coherence, enabling single-pass, instance-level editing.

Language-queried audio source separation (LASS) focuses on separating sounds using textual descriptions of the desired sources. Current methods mainly use discriminative approaches, such as time-frequency masking, to separate target sounds and minimize interference from other sources. However, these models face challenges when separating overlapping soundtracks, which may lead to artifacts such as spectral holes or incomplete separation. Rectified flow matching (RFM), a generative model that establishes linear relations between the distribution of data and noise, offers superior theoretical properties and simplicity, but has not yet been explored in sound separation. In this work, we introduce FlowSep, a new generative model based on RFM for LASS tasks. FlowSep learns linear flow trajectories from noise to target source features within the variational autoencoder (VAE) latent space. During inference, the RFM-generated latent features are reconstructed into a mel-spectrogram via the pre-trained VAE decoder, followed by a pre-trained vocoder to synthesize the waveform. Trained on 1,680 hours of audio data, FlowSep outperforms the state-of-the-art models across multiple benchmarks, as evaluated with subjective and objective metrics. Additionally, our results show that FlowSep surpasses a diffusion-based LASS model in both separation quality and inference efficiency, highlighting its strong potential for audio source separation tasks. Code, pre-trained models and demos can be found at: https://audio-agi.github.io/FlowSep_demo/.

Building efficient and effective generative models for neural network weights has been a research focus of significant interest that faces challenges posed by the high-dimensional weight spaces of modern neural networks and their symmetries. Several prior generative models are limited to generating partial neural network weights, particularly for larger models, such as ResNet and ViT. Those that do generate complete weights struggle with generation speed or require finetuning of the generated models. In this work, we present DeepWeightFlow, a Flow Matching model that operates directly in weight space to generate diverse and high-accuracy neural network weights for a variety of architectures, neural network sizes, and data modalities. The neural networks generated by DeepWeightFlow do not require fine-tuning to perform well and can scale to large networks. We apply Git Re-Basin and TransFusion for neural network canonicalization in the context of generative weight models to account for the impact of neural network permutation symmetries and to improve generation efficiency for larger model sizes. The generated networks excel at transfer learning, and ensembles of hundreds of neural networks can be generated in minutes, far exceeding the efficiency of diffusion-based methods. DeepWeightFlow models pave the way for more efficient and scalable generation of diverse sets of neural networks.

Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood on standard benchmarks. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient realistic-looking synthesis and manipulation of large images. The code for our model is available at https://github.com/openai/glow

State-of-the-art flow models achieve remarkable quality but require slow, iterative sampling. To accelerate this, flow maps can be distilled from pre-trained teachers, a procedure that conventionally requires sampling from an external dataset. We argue that this data-dependency introduces a fundamental risk of Teacher-Data Mismatch, as a static dataset may provide an incomplete or even misaligned representation of the teacher's full generative capabilities. This leads us to question whether this reliance on data is truly necessary for successful flow map distillation. In this work, we explore a data-free alternative that samples only from the prior distribution, a distribution the teacher is guaranteed to follow by construction, thereby circumventing the mismatch risk entirely. To demonstrate the practical viability of this philosophy, we introduce a principled framework that learns to predict the teacher's sampling path while actively correcting for its own compounding errors to ensure high fidelity. Our approach surpasses all data-based counterparts and establishes a new state-of-the-art by a significant margin. Specifically, distilling from SiT-XL/2+REPA, our method reaches an impressive FID of 1.45 on ImageNet 256x256, and 1.49 on ImageNet 512x512, both with only 1 sampling step. We hope our work establishes a more robust paradigm for accelerating generative models and motivates the broader adoption of flow map distillation without data.

Generative Adversarial Networks (GANs), especially the recent style-based generators (StyleGANs), have versatile semantics in the structured latent space. Latent semantics discovery methods emerge to move around the latent code such that only one factor varies during the traversal. Recently, an unsupervised method proposed a promising direction to directly use the eigenvectors of the projection matrix that maps latent codes to features as the interpretable directions. However, one overlooked fact is that the projection matrix is non-orthogonal and the number of eigenvectors is too large. The non-orthogonality would entangle semantic attributes in the top few eigenvectors, and the large dimensionality might result in meaningless variations among the directions even if the matrix is orthogonal. To avoid these issues, we propose Householder Projector, a flexible and general low-rank orthogonal matrix representation based on Householder transformations, to parameterize the projection matrix. The orthogonality guarantees that the eigenvectors correspond to disentangled interpretable semantics, while the low-rank property encourages that each identified direction has meaningful variations. We integrate our projector into pre-trained StyleGAN2/StyleGAN3 and evaluate the models on several benchmarks. Within only 1% of the original training steps for fine-tuning, our projector helps StyleGANs to discover more disentangled and precise semantic attributes without sacrificing image fidelity.

Conditional generative modeling aims to learn a conditional data distribution from samples containing data-condition pairs. For this, diffusion and flow-based methods have attained compelling results. These methods use a learned (flow) model to transport an initial standard Gaussian noise that ignores the condition to the conditional data distribution. The model is hence required to learn both mass transport and conditional injection. To ease the demand on the model, we propose Condition-Aware Reparameterization for Flow Matching (CAR-Flow) -- a lightweight, learned shift that conditions the source, the target, or both distributions. By relocating these distributions, CAR-Flow shortens the probability path the model must learn, leading to faster training in practice. On low-dimensional synthetic data, we visualize and quantify the effects of CAR. On higher-dimensional natural image data (ImageNet-256), equipping SiT-XL/2 with CAR-Flow reduces FID from 2.07 to 1.68, while introducing less than 0.6% additional parameters.

Flow Matching (FM) has recently emerged as a principled and efficient alternative to diffusion models. Standard FM encourages the learned velocity field to follow a target direction; however, it may accumulate errors along the trajectory and drive samples off the data manifold, leading to perceptual degradation, especially in lightweight or low-step configurations. To enhance stability and generalization, we extend FM into a balanced attract-repel scheme that provides explicit guidance on both "where to go" and "where not to go." To be formal, we propose Velocity Contrastive Regularization (VeCoR), a complementary training scheme for flow-based generative modeling that augments the standard FM objective with contrastive, two-sided supervision. VeCoR not only aligns the predicted velocity with a stable reference direction (positive supervision) but also pushes it away from inconsistent, off-manifold directions (negative supervision). This contrastive formulation transforms FM from a purely attractive, one-sided objective into a two-sided training signal, regularizing trajectory evolution and improving perceptual fidelity across datasets and backbones. On ImageNet-1K 256times256, VeCoR yields 22\% and 35\% relative FID reductions on SiT-XL/2 and REPA-SiT-XL/2 backbones, respectively, and achieves further FID gains (32\% relative) on MS-COCO text-to-image generation, demonstrating consistent improvements in stability, convergence, and image quality, particularly in low-step and lightweight settings. Project page: https://p458732.github.io/VeCoR_Project_Page/

We propose a 3D latent representation that jointly models object geometry and view-dependent appearance. Most prior works focus on either reconstructing 3D geometry or predicting view-independent diffuse appearance, and thus struggle to capture realistic view-dependent effects. Our approach leverages that RGB-depth images provide samples of a surface light field. By encoding random subsamples of this surface light field into a compact set of latent vectors, our model learns to represent both geometry and appearance within a unified 3D latent space. This representation reproduces view-dependent effects such as specular highlights and Fresnel reflections under complex lighting. We further train a latent flow matching model on this representation to learn its distribution conditioned on a single input image, enabling the generation of 3D objects with appearances consistent with the lighting and materials in the input. Experiments show that our approach achieves higher visual quality and better input fidelity than existing methods.

Flow matching is a powerful framework for generating high-quality samples in various applications, especially image synthesis. However, the intensive computational demands of these models, especially during the fine-tuning process and sampling processes, pose significant challenges for low-resource scenarios. This paper introduces Bellman Optimal Step-size Straightening (BOSS) technique for distilling flow-matching generative models: it aims specifically for a few-step efficient image sampling while adhering to a computational budget constraint. First, this technique involves a dynamic programming algorithm that optimizes the step sizes of the pretrained network. Then, it refines the velocity network to match the optimal step sizes, aiming to straighten the generation paths. Extensive experimental evaluations across image generation tasks demonstrate the efficacy of BOSS in terms of both resource utilization and image quality. Our results reveal that BOSS achieves substantial gains in efficiency while maintaining competitive sample quality, effectively bridging the gap between low-resource constraints and the demanding requirements of flow-matching generative models. Our paper also fortifies the responsible development of artificial intelligence, offering a more sustainable generative model that reduces computational costs and environmental footprints. Our code can be found at https://github.com/nguyenngocbaocmt02/BOSS.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a regularized mirror map that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-t prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-t priors and primal-space guarantees for constrained generation, under varepsilon-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.

Efficient deployment of small language models (SLMs) is essential for numerous real-world applications with stringent latency constraints. While previous work on SLM design has primarily focused on reducing the number of parameters to achieve parameter-optimal SLMs, parameter efficiency does not necessarily translate into proportional real-device speed-ups. This work aims to identify the key determinants of SLMs' real-device latency and offer generalizable principles and methodologies for SLM design and training when real-device latency is the primary consideration. Specifically, we identify two central architectural factors: depth-width ratios and operator choices. The former is crucial for small-batch-size latency, while the latter affects both latency and large-batch-size throughput. In light of this, we first study latency-optimal depth-width ratios, with the key finding that although deep-thin models generally achieve better accuracy under the same parameter budget, they may not lie on the accuracy-latency trade-off frontier. Next, we explore emerging efficient attention alternatives to evaluate their potential as candidate building operators. Using the identified promising operators, we construct an evolutionary search framework to automatically discover latency-optimal combinations of these operators within hybrid SLMs, thereby advancing the accuracy-latency frontier. In addition to architectural improvements, we further enhance SLM training using a weight normalization technique that enables more effective weight updates and improves final convergence. Combining these methods, we introduce a new family of hybrid SLMs, called Nemotron-Flash, which significantly advances the accuracy-efficiency frontier of state-of-the-art SLMs, e.g., achieving over +5.5% average accuracy, 1.3x/1.9x lower latency, and 18.7x/45.6x higher throughput compared to Qwen3-1.7B/0.6B, respectively.

Extracting optical flow from videos remains a core computer vision problem. Motivated by the success of large general-purpose models, we ask whether frozen self-supervised video models trained only for future frame prediction can be prompted, without fine-tuning, to output flow. Prior work reading out depth or illumination from video generators required fine-tuning, which is impractical for flow where labels are scarce and synthetic datasets suffer from a sim-to-real gap. Inspired by the Counterfactual World Model (CWM) paradigm, which can obtain point-wise correspondences by injecting a small tracer perturbation into a next-frame predictor and tracking its propagation, we extend this idea to generative video models. We explore several popular architectures and find that successful zero-shot flow extraction in this manner is aided by three model properties: (1) distributional prediction of future frames (avoiding blurry or noisy outputs); (2) factorized latents that treat each spatio-temporal patch independently; and (3) random-access decoding that can condition on any subset of future pixels. These properties are uniquely present in the recent Local Random Access Sequence (LRAS) architecture. Building on LRAS, we propose KL-tracing: a novel test-time procedure that injects a localized perturbation into the first frame, rolls out the model one step, and computes the Kullback-Leibler divergence between perturbed and unperturbed predictive distributions. Without any flow-specific fine-tuning, our method outperforms state-of-the-art models on real-world TAP-Vid DAVIS dataset (16.6% relative improvement for endpoint error) and synthetic TAP-Vid Kubric (4.7% relative improvement). Our results indicate that counterfactual prompting of controllable generative video models is a scalable and effective alternative to supervised or photometric-loss approaches for high-quality flow.

Latent variable models (LVMs) with discrete compositional latents are an important but challenging setting due to a combinatorially large number of possible configurations of the latents. A key tradeoff in modeling the posteriors over latents is between expressivity and tractable optimization. For algorithms based on expectation-maximization (EM), the E-step is often intractable without restrictive approximations to the posterior. We propose the use of GFlowNets, algorithms for sampling from an unnormalized density by learning a stochastic policy for sequential construction of samples, for this intractable E-step. By training GFlowNets to sample from the posterior over latents, we take advantage of their strengths as amortized variational inference algorithms for complex distributions over discrete structures. Our approach, GFlowNet-EM, enables the training of expressive LVMs with discrete compositional latents, as shown by experiments on non-context-free grammar induction and on images using discrete variational autoencoders (VAEs) without conditional independence enforced in the encoder.

MeanFlow has recently emerged as a powerful framework for few-step generative modeling trained from scratch, but its success is not yet fully understood. In this work, we show that the MeanFlow objective naturally decomposes into two parts: trajectory flow matching and trajectory consistency. Through gradient analysis, we find that these terms are strongly negatively correlated, causing optimization conflict and slow convergence. Motivated by these insights, we introduce alpha-Flow, a broad family of objectives that unifies trajectory flow matching, Shortcut Model, and MeanFlow under one formulation. By adopting a curriculum strategy that smoothly anneals from trajectory flow matching to MeanFlow, alpha-Flow disentangles the conflicting objectives, and achieves better convergence. When trained from scratch on class-conditional ImageNet-1K 256x256 with vanilla DiT backbones, alpha-Flow consistently outperforms MeanFlow across scales and settings. Our largest alpha-Flow-XL/2+ model achieves new state-of-the-art results using vanilla DiT backbones, with FID scores of 2.58 (1-NFE) and 2.15 (2-NFE).

Diffusion and flow-based non-autoregressive (NAR) models have shown strong promise in large language modeling, however, their potential for automatic speech recognition (ASR) remains largely unexplored. We propose Drax, a discrete flow matching framework for ASR that enables efficient parallel decoding. To better align training with inference, we construct an audio-conditioned probability path that guides the model through trajectories resembling likely intermediate inference errors, rather than direct random noise to target transitions. Our theoretical analysis links the generalization gap to divergences between training and inference occupancies, controlled by cumulative velocity errors, thereby motivating our design choice. Empirical evaluation demonstrates that our approach attains recognition accuracy on par with state-of-the-art speech models while offering improved accuracy-efficiency trade-offs, highlighting discrete flow matching as a promising direction for advancing NAR ASR.

We propose UniDFlow, a unified discrete flow-matching framework for multimodal understanding, generation, and editing. It decouples understanding and generation via task-specific low-rank adapters, avoiding objective interference and representation entanglement, while a novel reference-based multimodal preference alignment optimizes relative outcomes under identical conditioning, improving faithfulness and controllability without large-scale retraining. UniDFlpw achieves SOTA performance across eight benchmarks and exhibits strong zero-shot generalization to tasks including inpainting, in-context image generation, reference-based editing, and compositional generation, despite no explicit task-specific training.

The use of relative representations for latent embeddings has shown potential in enabling latent space communication and zero-shot model stitching across a wide range of applications. Nevertheless, relative representations rely on a certain amount of parallel anchors to be given as input, which can be impractical to obtain in certain scenarios. To overcome this limitation, we propose an optimization-based method to discover new parallel anchors from a limited known set (seed). Our approach can be used to find semantic correspondence between different domains, align their relative spaces, and achieve competitive results in several tasks.

Latent diffusion models (LDMs) power state-of-the-art high-resolution generative image models. LDMs learn the data distribution in the latent space of an autoencoder (AE) and produce images by mapping the generated latents into RGB image space using the AE decoder. While this approach allows for efficient model training and sampling, it induces a disconnect between the training of the diffusion model and the decoder, resulting in a loss of detail in the generated images. To remediate this disconnect, we propose to leverage the internal features of the decoder to define a latent perceptual loss (LPL). This loss encourages the models to create sharper and more realistic images. Our loss can be seamlessly integrated with common autoencoders used in latent diffusion models, and can be applied to different generative modeling paradigms such as DDPM with epsilon and velocity prediction, as well as flow matching. Extensive experiments with models trained on three datasets at 256 and 512 resolution show improved quantitative -- with boosts between 6% and 20% in FID -- and qualitative results when using our perceptual loss.

In this paper, we apply the self-attention from the state-of-the-art Transformer in Attention Is All You Need for the first time to a data-driven operator learning problem related to partial differential equations. An effort is put together to explain the heuristics of, and to improve the efficacy of the attention mechanism. By employing the operator approximation theory in Hilbert spaces, it is demonstrated for the first time that the softmax normalization in the scaled dot-product attention is sufficient but not necessary. Without softmax, the approximation capacity of a linearized Transformer variant can be proved to be comparable to a Petrov-Galerkin projection layer-wise, and the estimate is independent with respect to the sequence length. A new layer normalization scheme mimicking the Petrov-Galerkin projection is proposed to allow a scaling to propagate through attention layers, which helps the model achieve remarkable accuracy in operator learning tasks with unnormalized data. Finally, we present three operator learning experiments, including the viscid Burgers' equation, an interface Darcy flow, and an inverse interface coefficient identification problem. The newly proposed simple attention-based operator learner, Galerkin Transformer, shows significant improvements in both training cost and evaluation accuracy over its softmax-normalized counterparts.

We introduce CaLMFlow (Causal Language Models for Flow Matching), a novel framework that casts flow matching as a Volterra integral equation (VIE), leveraging the power of large language models (LLMs) for continuous data generation. CaLMFlow enables the direct application of LLMs to learn complex flows by formulating flow matching as a sequence modeling task, bridging discrete language modeling and continuous generative modeling. Our method implements tokenization across space and time, thereby solving a VIE over these domains. This approach enables efficient handling of high-dimensional data and outperforms ODE solver-dependent methods like conditional flow matching (CFM). We demonstrate CaLMFlow's effectiveness on synthetic and real-world data, including single-cell perturbation response prediction, showcasing its ability to incorporate textual context and generalize to unseen conditions. Our results highlight LLM-driven flow matching as a promising paradigm in generative modeling, offering improved scalability, flexibility, and context-awareness.

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator variance and inefficient sampling. Prior approaches mitigate this via explicit smoothness penalties, trajectory regularization, or modified probability paths and solvers. We introduce Temporal Pair Consistency (TPC), a lightweight variance-reduction principle that couples velocity predictions at paired timesteps along the same probability path, operating entirely at the estimator level without modifying the model architecture, probability path, or solver. We provide a theoretical analysis showing that TPC induces a quadratic, trajectory-coupled regularization that provably reduces gradient variance while preserving the underlying flow-matching objective. Instantiated within flow matching, TPC improves sample quality and efficiency across CIFAR-10 and ImageNet at multiple resolutions, achieving lower FID at identical or lower computational cost than prior methods, and extends seamlessly to modern SOTA-style pipelines with noise-augmented training, score-based denoising, and rectified flow.

Understanding and predicting motion is a fundamental component of visual intelligence. Although modern video models exhibit strong comprehension of scene dynamics, exploring multiple possible futures through full video synthesis remains prohibitively inefficient. We model scene dynamics orders of magnitude more efficiently by directly operating on a long-term motion embedding that is learned from large-scale trajectories obtained from tracker models. This enables efficient generation of long, realistic motions that fulfill goals specified via text prompts or spatial pokes. To achieve this, we first learn a highly compressed motion embedding with a temporal compression factor of 64x. In this space, we train a conditional flow-matching model to generate motion latents conditioned on task descriptions. The resulting motion distributions outperform those of both state-of-the-art video models and specialized task-specific approaches.

Recently, text-to-speech (TTS) models such as FastSpeech and ParaNet have been proposed to generate mel-spectrograms from text in parallel. Despite the advantage, the parallel TTS models cannot be trained without guidance from autoregressive TTS models as their external aligners. In this work, we propose Glow-TTS, a flow-based generative model for parallel TTS that does not require any external aligner. By combining the properties of flows and dynamic programming, the proposed model searches for the most probable monotonic alignment between text and the latent representation of speech on its own. We demonstrate that enforcing hard monotonic alignments enables robust TTS, which generalizes to long utterances, and employing generative flows enables fast, diverse, and controllable speech synthesis. Glow-TTS obtains an order-of-magnitude speed-up over the autoregressive model, Tacotron 2, at synthesis with comparable speech quality. We further show that our model can be easily extended to a multi-speaker setting.

Inversion-based image editing in flow matching models has emerged as a powerful paradigm for training-free, text-guided image manipulation. A central challenge in this paradigm is the injection dilemma: injecting source features during denoising preserves the background of the original image but simultaneously suppresses the model's ability to synthesize edited content. Existing methods address this with fixed injection strategies -- binary on/off temporal schedules, uniform spatial mixing ratios, and channel-agnostic latent perturbation -- that ignore the inherently heterogeneous nature of injection demand across both the temporal and channel dimensions. In this paper, we present AdaEdit, a training-free adaptive editing framework that resolves this dilemma through two complementary innovations. First, we propose a Progressive Injection Schedule that replaces hard binary cutoffs with continuous decay functions (sigmoid, cosine, or linear), enabling a smooth transition from source-feature preservation to target-feature generation and eliminating feature discontinuity artifacts. Second, we introduce Channel-Selective Latent Perturbation, which estimates per-channel importance based on the distributional gap between the inverted and random latents and applies differentiated perturbation strengths accordingly -- strongly perturbing edit-relevant channels while preserving structure-encoding channels. Extensive experiments on the PIE-Bench benchmark (700 images, 10 editing types) demonstrate that AdaEdit achieves an 8.7% reduction in LPIPS, a 2.6% improvement in SSIM, and a 2.3% improvement in PSNR over strong baselines, while maintaining competitive CLIP similarity. AdaEdit is fully plug-and-play and compatible with multiple ODE solvers including Euler, RF-Solver, and FireFlow. Code is available at https://github.com/leeguandong/AdaEdit

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between representations and ensuring compatibility across independently trained neural networks. In the literature, two primary approaches are commonly used to adapt different learned representations: affine transformations, which adapt well to specific distributions but can significantly alter the original representation, and orthogonal transformations, which preserve the original structure with strict geometric constraints but limit adaptability. A key challenge is adapting the latent spaces of updated models to align with those of previous models on downstream distributions while preserving the newly learned representation spaces. In this paper, we impose a relaxed orthogonality constraint, namely λ-Orthogonality regularization, while learning an affine transformation, to obtain distribution-specific adaptation while retaining the original learned representations. Extensive experiments across various architectures and datasets validate our approach, demonstrating that it preserves the model's zero-shot performance and ensures compatibility across model updates. Code available at: https://github.com/miccunifi/lambda_orthogonality.git{https://github.com/miccunifi/lambda\_orthogonality}.

To advance continuous-valued token modeling and temporal-coherence enforcement, we propose FELLE, an autoregressive model that integrates language modeling with token-wise flow matching. By leveraging the autoregressive nature of language models and the generative efficacy of flow matching, FELLE effectively predicts continuous-valued tokens (mel-spectrograms). For each continuous-valued token, FELLE modifies the general prior distribution in flow matching by incorporating information from the previous step, improving coherence and stability. Furthermore, to enhance synthesis quality, FELLE introduces a coarse-to-fine flow-matching mechanism, generating continuous-valued tokens hierarchically, conditioned on the language model's output. Experimental results demonstrate the potential of incorporating flow-matching techniques in autoregressive mel-spectrogram modeling, leading to significant improvements in TTS generation quality, as shown in https://aka.ms/felle.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise. Injective Flows fix this by jointly learning a manifold and the distribution on it. So far, they have been limited by restrictive architectures and/or high computational cost. We lift both constraints by a new efficient estimator for the maximum likelihood loss, compatible with free-form bottleneck architectures. We further show that naively learning both the data manifold and the distribution on it can lead to divergent solutions, and use this insight to motivate a stable maximum likelihood training objective. We perform extensive experiments on toy, tabular and image data, demonstrating the competitive performance of the resulting model.

Generative modeling has recently achieved remarkable success across image, video, and audio domains, demonstrating powerful capabilities for unified representation learning. Yet speech front-end tasks such as speech enhancement (SE), target speaker extraction (TSE), acoustic echo cancellation (AEC), and language-queried source separation (LASS) remain largely tackled by disparate, task-specific solutions. This fragmentation leads to redundant engineering effort, inconsistent performance, and limited extensibility. To address this gap, we introduce UniFlow, a unified framework that employs continuous generative modeling to tackle diverse speech front-end tasks in a shared latent space. Specifically, UniFlow utilizes a waveform variational autoencoder (VAE) to learn a compact latent representation of raw audio, coupled with a Diffusion Transformer (DiT) that predicts latent updates. To differentiate the speech processing task during the training, learnable condition embeddings indexed by a task ID are employed to enable maximal parameter sharing while preserving task-specific adaptability. To balance model performance and computational efficiency, we investigate and compare three generative objectives: denoising diffusion, flow matching, and mean flow within the latent domain. We validate UniFlow on multiple public benchmarks, demonstrating consistent gains over state-of-the-art baselines. UniFlow's unified latent formulation and conditional design make it readily extensible to new tasks, providing an integrated foundation for building and scaling generative speech processing pipelines. To foster future research, we will open-source our codebase.

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by optimizing EBFlow with score-matching objectives, the computation of Jacobian determinants for linear transformations can be entirely bypassed. This feature enables the use of arbitrary linear layers in the construction of flow-based models without increasing the computational time complexity of each training iteration from O(D^2L) to O(D^3L) for an L-layered model that accepts D-dimensional inputs. This makes the training of EBFlow more efficient than the commonly-adopted maximum likelihood training method. In addition to the reduction in runtime, we enhance the training stability and empirical performance of EBFlow through a number of techniques developed based on our analysis of the score-matching methods. The experimental results demonstrate that our approach achieves a significant speedup compared to maximum likelihood estimation while outperforming prior methods with a noticeable margin in terms of negative log-likelihood (NLL).

Advances in deep learning have significantly enhanced medical image analysis, yet the availability of large-scale medical datasets remains constrained by patient privacy concerns. We present EchoFlow, a novel framework designed to generate high-quality, privacy-preserving synthetic echocardiogram images and videos. EchoFlow comprises four key components: an adversarial variational autoencoder for defining an efficient latent representation of cardiac ultrasound images, a latent image flow matching model for generating accurate latent echocardiogram images, a latent re-identification model to ensure privacy by filtering images anatomically, and a latent video flow matching model for animating latent images into realistic echocardiogram videos conditioned on ejection fraction. We rigorously evaluate our synthetic datasets on the clinically relevant task of ejection fraction regression and demonstrate, for the first time, that downstream models trained exclusively on EchoFlow-generated synthetic datasets achieve performance parity with models trained on real datasets. We release our models and synthetic datasets, enabling broader, privacy-compliant research in medical ultrasound imaging at https://huggingface.co/spaces/HReynaud/EchoFlow.

Advanced generative models excel at synthesizing images but often rely on text-based conditioning. Visual designers, however, often work beyond language, directly drawing inspiration from existing visual elements. In many cases, these elements represent only fragments of a potential concept-such as an uniquely structured wing, or a specific hairstyle-serving as inspiration for the artist to explore how they can come together creatively into a coherent whole. Recognizing this need, we introduce a generative framework that seamlessly integrates a partial set of user-provided visual components into a coherent composition while simultaneously sampling the missing parts needed to generate a plausible and complete concept. Our approach builds on a strong and underexplored representation space, extracted from IP-Adapter+, on which we train IP-Prior, a lightweight flow-matching model that synthesizes coherent compositions based on domain-specific priors, enabling diverse and context-aware generations. Additionally, we present a LoRA-based fine-tuning strategy that significantly improves prompt adherence in IP-Adapter+ for a given task, addressing its common trade-off between reconstruction quality and prompt adherence.

Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time. Flow map models, commonly known as consistency models, encompass many recent efforts to improve inference-time efficiency by learning the solution operator of this differential equation. Yet despite their promise, these models lack a unified description that clearly explains how to learn them efficiently in practice. Here, building on the methodology proposed in Boffi et. al. (2024), we present a systematic algorithmic framework for directly learning the flow map associated with a flow or diffusion model. By exploiting a relationship between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map, we show how to convert any distillation scheme into a direct training algorithm via self-distillation, eliminating the need for pre-trained teachers. We introduce three algorithmic families based on different mathematical characterizations of the flow map: Eulerian, Lagrangian, and Progressive methods, which we show encompass and extend all known distillation and direct training schemes for consistency models. We find that the novel class of Lagrangian methods, which avoid both spatial derivatives and bootstrapping from small steps by design, achieve significantly more stable training and higher performance than more standard Eulerian and Progressive schemes. Our methodology unifies existing training schemes under a single common framework and reveals new design principles for accelerated generative modeling. Associated code is available at https://github.com/nmboffi/flow-maps.

Efficient training strategies for large-scale diffusion models have recently emphasized the importance of improving discriminative feature representations in these models. A central line of work in this direction is representation alignment with features obtained from powerful external encoders, which improves the representation quality as assessed through linear probing. Alignment-based approaches show promise but depend on large pretrained encoders, which are computationally expensive to obtain. In this work, we propose an alternative regularization for training, based on promoting the Linear SEParability (LSEP) of intermediate layer representations. LSEP eliminates the need for an auxiliary encoder and representation alignment, while incorporating linear probing directly into the network's learning dynamics rather than treating it as a simple post-hoc evaluation tool. Our results demonstrate substantial improvements in both training efficiency and generation quality on flow-based transformer architectures such as SiTs, achieving an FID of 1.46 on 256 times 256 ImageNet dataset.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

Flow Matching (FM) algorithm achieves remarkable results in generative tasks especially in robotic manipulation. Building upon the foundations of diffusion models, the simulation-free paradigm of FM enables simple and efficient training, but inherently introduces a train-inference gap. Specifically, we cannot assess the model's output during the training phase. In contrast, other generative models including Variational Autoencoder (VAE), Normalizing Flow and Generative Adversarial Networks (GANs) directly optimize on the reconstruction loss. Such a gap is particularly evident in scenarios that demand high precision, such as robotic manipulation. Moreover, we show that FM's over-pursuit of straight predefined paths may introduce some serious problems such as stiffness into the system. These motivate us to fine-tune FM via Maximum Likelihood Estimation of reconstructions - an approach made feasible by FM's underlying smooth ODE formulation, in contrast to the stochastic differential equations (SDEs) used in diffusion models. This paper first theoretically analyzes the relation between training loss and inference error in FM. Then we propose a method of fine-tuning FM via Maximum Likelihood Estimation of reconstructions, which includes both straightforward fine-tuning and residual-based fine-tuning approaches. Furthermore, through specifically designed architectures, the residual-based fine-tuning can incorporate the contraction property into the model, which is crucial for the model's robustness and interpretability. Experimental results in image generation and robotic manipulation verify that our method reliably improves the inference performance of FM.

Scene flow estimation is a long-standing problem in computer vision, where the goal is to find the 3D motion of a scene from its consecutive observations. Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset. We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available at https://github.com/itailang/SCOOP.

Diffusion- and flow-based models have emerged as state-of-the-art generative modeling approaches, but they require many sampling steps. Consistency models can distill these models into efficient one-step generators; however, unlike flow- and diffusion-based methods, their performance inevitably degrades when increasing the number of steps, which we show both analytically and empirically. Flow maps generalize these approaches by connecting any two noise levels in a single step and remain effective across all step counts. In this paper, we introduce two new continuous-time objectives for training flow maps, along with additional novel training techniques, generalizing existing consistency and flow matching objectives. We further demonstrate that autoguidance can improve performance, using a low-quality model for guidance during distillation, and an additional boost can be achieved by adversarial finetuning, with minimal loss in sample diversity. We extensively validate our flow map models, called Align Your Flow, on challenging image generation benchmarks and achieve state-of-the-art few-step generation performance on both ImageNet 64x64 and 512x512, using small and efficient neural networks. Finally, we show text-to-image flow map models that outperform all existing non-adversarially trained few-step samplers in text-conditioned synthesis.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG). To address these limitations, we propose a novel Gaussian mixture flow matching (GMFlow) model: instead of predicting the mean, GMFlow predicts dynamic Gaussian mixture (GM) parameters to capture a multi-modal flow velocity distribution, which can be learned with a KL divergence loss. We demonstrate that GMFlow generalizes previous diffusion and flow matching models where a single Gaussian is learned with an L_2 denoising loss. For inference, we derive GM-SDE/ODE solvers that leverage analytic denoising distributions and velocity fields for precise few-step sampling. Furthermore, we introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality. Extensive experiments demonstrate that GMFlow consistently outperforms flow matching baselines in generation quality, achieving a Precision of 0.942 with only 6 sampling steps on ImageNet 256times256.

We present an ultra-efficient post-training method for shortcutting large-scale pre-trained flow matching diffusion models into efficient few-step samplers, enabled by novel velocity field self-distillation. While shortcutting in flow matching, originally introduced by shortcut models, offers flexible trajectory-skipping capabilities, it requires a specialized step-size embedding incompatible with existing models unless retraining from scratchx2013a process nearly as costly as pretraining itself. Our key contribution is thus imparting a more aggressive shortcut mechanism to standard flow matching models (e.g., Flux), leveraging a unique distillation principle that obviates the need for step-size embedding. Working on the velocity field rather than sample space and learning rapidly from self-guided distillation in an online manner, our approach trains efficiently, e.g., producing a 3-step Flux less than one A100 day. Beyond distillation, our method can be incorporated into the pretraining stage itself, yielding models that inherently learn efficient, few-step flows without compromising quality. This capability also enables, to our knowledge, the first few-shot distillation method (e.g., 10 text-image pairs) for dozen-billion-parameter diffusion models, delivering state-of-the-art performance at almost free cost.

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from scratch. By analyzing the relationship between the velocity function and the solution function of the velocity ordinary differential equation (ODE), we propose a Flow Matching loss and a solution consistency loss to train our models. The Flow Matching loss allows our models to provide estimated velocity fields for Classifier-Free Guidance (CFG) during training, which improves generation performance. Notably, our consistency loss does not require the calculation of the Jacobian-vector product (JVP), a common requirement in recent works that is not well-optimized in deep learning frameworks like PyTorch. Experimental results indicate that, when trained from scratch using the same Diffusion Transformer (DiT) architecture and an equal number of training epochs, our models achieve better FID-50K scores than MeanFlow models on the ImageNet 256x256 dataset.

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While functional generative models are theoretically domain- and discretization-agnostic, current implementations heavily rely on the Fourier Neural Operator (FNO), limiting their applicability to regular grids and rectangular domains. To overcome these critical limitations, we introduce the Mesh-Informed Neural Operator (MINO). By leveraging graph neural operators and cross-attention mechanisms, MINO offers a principled, domain- and discretization-agnostic backbone for generative modeling in function spaces. This advancement significantly expands the scope of such models to more diverse applications in generative, inverse, and regression tasks. Furthermore, MINO provides a unified perspective on integrating neural operators with general advanced deep learning architectures. Finally, we introduce a suite of standardized evaluation metrics that enable objective comparison of functional generative models, addressing another critical gap in the field.

The ability to learn multi-modal action distributions is indispensable for robotic manipulation policies to perform precise and robust control. Flow-based generative models have recently emerged as a promising solution to learning distributions of actions, offering one-step action generation and thus achieving much higher sampling efficiency compared to diffusion-based methods. However, existing flow-based policies suffer from representation collapse, the inability to distinguish similar visual representations, leading to failures in precise manipulation tasks. We propose DM1 (MeanFlow with Dispersive Regularization for One-Step Robotic Manipulation), a novel flow matching framework that integrates dispersive regularization into MeanFlow to prevent collapse while maintaining one-step efficiency. DM1 employs multiple dispersive regularization variants across different intermediate embedding layers, encouraging diverse representations across training batches without introducing additional network modules or specialized training procedures. Experiments on RoboMimic benchmarks show that DM1 achieves 20-40 times faster inference (0.07s vs. 2-3.5s) and improves success rates by 10-20 percentage points, with the Lift task reaching 99% success over 85% of the baseline. Real-robot deployment on a Franka Panda further validates that DM1 transfers effectively from simulation to the physical world. To the best of our knowledge, this is the first work to leverage representation regularization to enable flow-based policies to achieve strong performance in robotic manipulation, establishing a simple yet powerful approach for efficient and robust manipulation.

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

Large language models can generate fluent answers that are unfaithful to the provided context, while many safeguards rely on external verification or a separate judge after generation. We introduce internal flow signatures that audit decision formation from depthwise dynamics at a fixed inter-block monitoring boundary. The method stabilizes token-wise motion via bias-centered monitoring, then summarizes trajectories in compact moving readout-aligned subspaces constructed from the top token and its close competitors within each depth window. Neighboring window frames are aligned by an orthogonal transport, yielding depth-comparable transported step lengths, turning angles, and subspace drift summaries that are invariant to within-window basis choices. A lightweight GRU validator trained on these signatures performs self-checking without modifying the base model. Beyond detection, the validator localizes a culprit depth event and enables a targeted refinement: the model rolls back to the culprit token and clamps an abnormal transported step at the identified block while preserving the orthogonal residual. The resulting pipeline provides actionable localization and low-overhead self-checking from internal decision dynamics. Code is available at github.com/EavnJeong/Internal-Flow-Signatures-for-Self-Checking-and-Refinement-in-LLMs.

In this paper, we introduce Latent Bridge Matching (LBM), a new, versatile and scalable method that relies on Bridge Matching in a latent space to achieve fast image-to-image translation. We show that the method can reach state-of-the-art results for various image-to-image tasks using only a single inference step. In addition to its efficiency, we also demonstrate the versatility of the method across different image translation tasks such as object removal, normal and depth estimation, and object relighting. We also derive a conditional framework of LBM and demonstrate its effectiveness by tackling the tasks of controllable image relighting and shadow generation. We provide an open-source implementation of the method at https://github.com/gojasper/LBM.

Consistency Training (CT) has recently emerged as a promising alternative to diffusion models, achieving competitive performance in image generation tasks. However, non-distillation consistency training often suffers from high variance and instability, and analyzing and improving its training dynamics is an active area of research. In this work, we propose a novel CT training approach based on the Flow Matching framework. Our main contribution is a trained noise-coupling scheme inspired by the architecture of Variational Autoencoders (VAE). By training a data-dependent noise emission model implemented as an encoder architecture, our method can indirectly learn the geometry of the noise-to-data mapping, which is instead fixed by the choice of the forward process in classical CT. Empirical results across diverse image datasets show significant generative improvements, with our model outperforming baselines and achieving the state-of-the-art (SoTA) non-distillation CT FID on CIFAR-10, and attaining FID on par with SoTA on ImageNet at 64 times 64 resolution in 2-step generation. Our code is available at https://github.com/sony/vct .

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems show that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

We propose a new approach to vision-based dexterous grasp translation, which aims to transfer grasp intent across robotic hands with differing morphologies. Given a visual observation of a source hand grasping an object, our goal is to synthesize a functionally equivalent grasp for a target hand without requiring paired demonstrations or hand-specific simulations. We frame this problem as a stochastic transport between grasp distributions using the Schrödinger Bridge formalism. Our method learns to map between source and target latent grasp spaces via score and flow matching, conditioned on visual observations. To guide this translation, we introduce physics-informed cost functions that encode alignment in base pose, contact maps, wrench space, and manipulability. Experiments across diverse hand-object pairs demonstrate our approach generates stable, physically grounded grasps with strong generalization. This work enables semantic grasp transfer for heterogeneous manipulators and bridges vision-based grasping with probabilistic generative modeling. Additional details at https://grasp2grasp.github.io/

Probabilistic Circuits (PCs) are a unified framework for tractable probabilistic models that support efficient computation of various probabilistic queries (e.g., marginal probabilities). One key challenge is to scale PCs to model large and high-dimensional real-world datasets: we observe that as the number of parameters in PCs increases, their performance immediately plateaus. This phenomenon suggests that the existing optimizers fail to exploit the full expressive power of large PCs. We propose to overcome such bottleneck by latent variable distillation: we leverage the less tractable but more expressive deep generative models to provide extra supervision over the latent variables of PCs. Specifically, we extract information from Transformer-based generative models to assign values to latent variables of PCs, providing guidance to PC optimizers. Experiments on both image and language modeling benchmarks (e.g., ImageNet and WikiText-2) show that latent variable distillation substantially boosts the performance of large PCs compared to their counterparts without latent variable distillation. In particular, on the image modeling benchmarks, PCs achieve competitive performance against some of the widely-used deep generative models, including variational autoencoders and flow-based models, opening up new avenues for tractable generative modeling.

Vision-Language-Action (VLA) models trained with flow matching have demonstrated impressive capabilities on robotic manipulation tasks. However, their performance often degrades under distribution shift and on complex multi-step tasks, suggesting that the learned representations may not robustly capture task-relevant semantics. We introduce DiG-Flow, a principled framework that enhances VLA robustness through geometric regularization. Our key insight is that the distributional discrepancy between observation and action embeddings provides a meaningful geometric signal: lower transport cost indicates compatible representations, while higher cost suggests potential misalignment. DiG-Flow computes a discrepancy measure between empirical distributions of observation and action embeddings, maps it to a modulation weight via a monotone function, and applies residual updates to the observation embeddings before flow matching. Crucially, this intervention operates at the representation level without modifying the flow matching path or target vector field. We provide theoretical guarantees showing that discrepancy-guided training provably decreases the training objective, and that guided inference refinement converges with contraction. Empirically, DiG-Flow integrates into existing VLA architectures with negligible overhead and consistently improves performance, with particularly pronounced gains on complex multi-step tasks and under limited training data.

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards the conditional velocity field. However, on constrained domains, the learned velocity model may lead to undesirable flows that result in highly unnatural samples, e.g., oversaturated images, due to both flow matching error and simulation error. To address this, we add a boundary constraint term to CNFs, which leads to reflected CNFs that keep trajectories within the constrained domains. We propose reflected flow matching (RFM) to train the velocity model in reflected CNFs by matching the conditional velocity fields in a simulation-free manner, similar to the vanilla FM. Moreover, the analytical form of conditional velocity fields in RFM avoids potentially biased approximations, making it superior to existing score-based generative models on constrained domains. We demonstrate that RFM achieves comparable or better results on standard image benchmarks and produces high-quality class-conditioned samples under high guidance weight.

Conditional image-to-video (cI2V) generation aims to synthesize a new plausible video starting from an image (e.g., a person's face) and a condition (e.g., an action class label like smile). The key challenge of the cI2V task lies in the simultaneous generation of realistic spatial appearance and temporal dynamics corresponding to the given image and condition. In this paper, we propose an approach for cI2V using novel latent flow diffusion models (LFDM) that synthesize an optical flow sequence in the latent space based on the given condition to warp the given image. Compared to previous direct-synthesis-based works, our proposed LFDM can better synthesize spatial details and temporal motion by fully utilizing the spatial content of the given image and warping it in the latent space according to the generated temporally-coherent flow. The training of LFDM consists of two separate stages: (1) an unsupervised learning stage to train a latent flow auto-encoder for spatial content generation, including a flow predictor to estimate latent flow between pairs of video frames, and (2) a conditional learning stage to train a 3D-UNet-based diffusion model (DM) for temporal latent flow generation. Unlike previous DMs operating in pixel space or latent feature space that couples spatial and temporal information, the DM in our LFDM only needs to learn a low-dimensional latent flow space for motion generation, thus being more computationally efficient. We conduct comprehensive experiments on multiple datasets, where LFDM consistently outperforms prior arts. Furthermore, we show that LFDM can be easily adapted to new domains by simply finetuning the image decoder. Our code is available at https://github.com/nihaomiao/CVPR23_LFDM.

Real-world text applications often involve composing a wide range of text control operations, such as editing the text w.r.t. an attribute, manipulating keywords and structure, and generating new text of desired properties. Prior work typically learns/finetunes a language model (LM) to perform individual or specific subsets of operations. Recent research has studied combining operations in a plug-and-play manner, often with costly search or optimization in the complex sequence space. This paper proposes a new efficient approach for composable text operations in the compact latent space of text. The low-dimensionality and differentiability of the text latent vector allow us to develop an efficient sampler based on ordinary differential equations (ODEs) given arbitrary plug-in operators (e.g., attribute classifiers). By connecting pretrained LMs (e.g., GPT2) to the latent space through efficient adaption, we then decode the sampled vectors into desired text sequences. The flexible approach permits diverse control operators (sentiment, tense, formality, keywords, etc.) acquired using any relevant data from different domains. Experiments show that composing those operators within our approach manages to generate or edit high-quality text, substantially improving over previous methods in terms of generation quality and efficiency.

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new samples from this space. This characteristic creates an intrinsic synergy between representation learning and data generation. However, the generative quality of standard NFs is limited by poor semantic representations from log-likelihood optimization. To remedy this, we propose a novel alignment strategy that creatively leverages the invertibility of NFs: instead of regularizing the forward pass, we align the intermediate features of the generative (reverse) pass with representations from a powerful vision foundation model, demonstrating superior effectiveness over naive alignment. We also introduce a novel training-free, test-time optimization algorithm for classification, which provides a more intrinsic evaluation of the NF's embedded semantic knowledge. Comprehensive experiments demonstrate that our approach accelerates the training of NFs by over 3.3times, while simultaneously delivering significant improvements in both generative quality and classification accuracy. New state-of-the-art results for NFs are established on ImageNet 64times64 and 256times256. Our code is available at https://github.com/MCG-NJU/FlowBack.

Large Language Models (LLMs) are primarily designed for batch processing. Existing methods for adapting LLMs to streaming rely either on expensive re-encoding or specialized architectures with limited scalability. This work identifies three key mismatches in adapting batch-oriented LLMs to streaming: (1) input-attention, (2) output-attention, and (3) position-ID mismatches. While it is commonly assumed that the latter two mismatches require frequent re-encoding, our analysis reveals that only the input-attention mismatch significantly impacts performance, indicating re-encoding outputs is largely unnecessary. To better understand this discrepancy with the common assumption, we provide the first comprehensive analysis of the impact of position encoding on LLMs in streaming, showing that preserving relative positions within source and target contexts is more critical than maintaining absolute order. Motivated by the above analysis, we introduce a group position encoding paradigm built on batch architectures to enhance consistency between streaming and batch modes. Extensive experiments on cross-lingual and cross-modal tasks demonstrate that our method outperforms existing approaches. Our method requires no architectural modifications, exhibits strong generalization in both streaming and batch modes. The code is available at repository https://github.com/EIT-NLP/StreamingLLM.

Current feed-forward 3D/4D reconstruction systems rely on dense geometry and pose supervision -- expensive to obtain at scale and particularly scarce for dynamic real-world scenes. We present Flow3r, a framework that augments visual geometry learning with dense 2D correspondences (`flow') as supervision, enabling scalable training from unlabeled monocular videos. Our key insight is that the flow prediction module should be factored: predicting flow between two images using geometry latents from one and pose latents from the other. This factorization directly guides the learning of both scene geometry and camera motion, and naturally extends to dynamic scenes. In controlled experiments, we show that factored flow prediction outperforms alternative designs and that performance scales consistently with unlabeled data. Integrating factored flow into existing visual geometry architectures and training with {sim}800K unlabeled videos, Flow3r achieves state-of-the-art results across eight benchmarks spanning static and dynamic scenes, with its largest gains on in-the-wild dynamic videos where labeled data is most scarce.

Diffusion transformers (DiTs) achieve high generative quality but lock FLOPs to image resolution, limiting principled latency-quality trade-offs, and allocate computation uniformly across input spatial tokens, wasting resource allocation to unimportant regions. We introduce Elastic Latent Interface Transformer (ELIT), a drop-in, DiT-compatible mechanism that decouples input image size from compute. Our approach inserts a latent interface, a learnable variable-length token sequence on which standard transformer blocks can operate. Lightweight Read and Write cross-attention layers move information between spatial tokens and latents and prioritize important input regions. By training with random dropping of tail latents, ELIT learns to produce importance-ordered representations with earlier latents capturing global structure while later ones contain information to refine details. At inference, the number of latents can be dynamically adjusted to match compute constraints. ELIT is deliberately minimal, adding two cross-attention layers while leaving the rectified flow objective and the DiT stack unchanged. Across datasets and architectures (DiT, U-ViT, HDiT, MM-DiT), ELIT delivers consistent gains. On ImageNet-1K 512px, ELIT delivers an average gain of 35.3% and 39.6% in FID and FDD scores. Project page: https://snap-research.github.io/elit/

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

The emergence of similar representations between independently trained neural models has sparked significant interest in the representation learning community, leading to the development of various methods to obtain communication between latent spaces. "Latent space communication" can be achieved in two ways: i) by independently mapping the original spaces to a shared or relative one; ii) by directly estimating a transformation from a source latent space to a target one. In this work, we combine the two into a novel method to obtain latent space translation through the relative space. By formalizing the invertibility of angle-preserving relative representations and assuming the scale invariance of decoder modules in neural models, we can effectively use the relative space as an intermediary, independently projecting onto and from other semantically similar spaces. Extensive experiments over various architectures and datasets validate our scale invariance assumption and demonstrate the high accuracy of our method in latent space translation. We also apply our method to zero-shot stitching between arbitrary pre-trained text and image encoders and their classifiers, even across modalities. Our method has significant potential for facilitating the reuse of models in a practical manner via compositionality.

We present FlowDet, the first formulation of object detection using modern Conditional Flow Matching techniques. This work follows from DiffusionDet, which originally framed detection as a generative denoising problem in the bounding box space via diffusion. We revisit and generalise this formulation to a broader class of generative transport problems, while maintaining the ability to vary the number of boxes and inference steps without re-training. In contrast to the curved stochastic transport paths induced by diffusion, FlowDet learns simpler and straighter paths resulting in faster scaling of detection performance as the number of inference steps grows. We find that this reformulation enables us to outperform diffusion based detection systems (as well as non-generative baselines) across a wide range of experiments, including various precision/recall operating points using multiple feature backbones and datasets. In particular, when evaluating under recall-constrained settings, we can highlight the effects of the generative transport without over-compensating with large numbers of proposals. This provides gains of up to +3.6% AP and +4.2% AP_{rare} over DiffusionDet on the COCO and LVIS datasets, respectively.

Previous text-guided video editing methods often suffer from temporal inconsistency, motion distortion, and-most notably-limited domain transformation. We attribute these limitations to insufficient modeling of spatiotemporal pixel relevance during the editing process. To address this, we propose STR-Match, a training-free video editing algorithm that produces visually appealing and spatiotemporally coherent videos through latent optimization guided by our novel STR score. The score captures spatiotemporal pixel relevance across adjacent frames by leveraging 2D spatial attention and 1D temporal modules in text-to-video (T2V) diffusion models, without the overhead of computationally expensive 3D attention mechanisms. Integrated into a latent optimization framework with a latent mask, STR-Match generates temporally consistent and visually faithful videos, maintaining strong performance even under significant domain transformations while preserving key visual attributes of the source. Extensive experiments demonstrate that STR-Match consistently outperforms existing methods in both visual quality and spatiotemporal consistency.

This paper focuses on the alignment of flow matching models with human preferences. A promising way is fine-tuning by directly backpropagating reward gradients through the differentiable generation process of flow matching. However, backpropagating through long trajectories results in prohibitive memory costs and gradient explosion. Therefore, direct-gradient methods struggle to update early generation steps, which are crucial for determining the global structure of the final image. To address this issue, we introduce LeapAlign, a fine-tuning method that reduces computational cost and enables direct gradient propagation from reward to early generation steps. Specifically, we shorten the long trajectory into only two steps by designing two consecutive leaps, each skipping multiple ODE sampling steps and predicting future latents in a single step. By randomizing the start and end timesteps of the leaps, LeapAlign leads to efficient and stable model updates at any generation step. To better use such shortened trajectories, we assign higher training weights to those that are more consistent with the long generation path. To further enhance gradient stability, we reduce the weights of gradient terms with large magnitude, instead of completely removing them as done in previous works. When fine-tuning the Flux model, LeapAlign consistently outperforms state-of-the-art GRPO-based and direct-gradient methods across various metrics, achieving superior image quality and image-text alignment.

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

The space of task-agnostic feature upsampling has emerged as a promising area of research to efficiently create denser features from pre-trained visual backbones. These methods act as a shortcut to achieve dense features for a fraction of the cost by learning to map low-resolution features to high-resolution versions. While early works in this space used iterative upsampling approaches, more recent works have switched to cross-attention-based methods, which risk falling into the same efficiency scaling problems of the backbones they are upsampling. In this work, we demonstrate that iterative upsampling methods can still compete with cross-attention-based methods; moreover, they can achieve state-of-the-art performance with lower inference costs. We propose UPLiFT, an architecture for Universal Pixel-dense Lightweight Feature Transforms. We also propose an efficient Local Attender operator to overcome the limitations of prior iterative feature upsampling methods. This operator uses an alternative attentional pooling formulation defined fully locally. We show that our Local Attender allows UPLiFT to maintain stable features throughout upsampling, enabling state-of-the-art performance with lower inference costs than existing pixel-dense feature upsamplers. In addition, we apply UPLiFT to generative downstream tasks and show that it achieves competitive performance with state-of-the-art Coupled Flow Matching models for VAE feature upsampling. Altogether, UPLiFT offers a versatile and efficient approach to creating denser features.

Neural operators, as an efficient surrogate model for learning the solutions of PDEs, have received extensive attention in the field of scientific machine learning. Among them, attention-based neural operators have become one of the mainstreams in related research. However, existing approaches overfit the limited training data due to the considerable number of parameters in the attention mechanism. To address this, we develop an orthogonal attention based on the eigendecomposition of the kernel integral operator and the neural approximation of eigenfunctions. The orthogonalization naturally poses a proper regularization effect on the resulting neural operator, which aids in resisting overfitting and boosting generalization. Experiments on six standard neural operator benchmark datasets comprising both regular and irregular geometries show that our method can outperform competing baselines with decent margins.

World models have demonstrated impressive performance on robotic learning tasks. Many such tasks inherently demand multimodal reasoning; for example, filling a bottle with water will lead to visual information alone being ambiguous or incomplete, thereby requiring reasoning over the temporal evolution of audio, accounting for its underlying physical properties and pitch patterns. In this paper, we propose a generative latent flow matching model to anticipate future audio observations, enabling the system to reason about long-term consequences when integrated into a robot policy. We demonstrate the superior capabilities of our system through two manipulation tasks that require perceiving in-the-wild audio or music signals, compared to methods without future lookahead. We further emphasize that successful robot action learning for these tasks relies not merely on multi-modal input, but critically on the accurate prediction of future audio states that embody intrinsic rhythmic patterns.

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis. By framing neural networks as operators with fixed points representing desired solutions, we develop a theoretical framework grounded in iterative methods for operator equations. Under defined conditions, we present convergence proofs based on fixed point theory. We demonstrate that popular architectures, such as diffusion models and AlphaFold, inherently employ iterative operator learning. Empirical assessments highlight that performing iterations through network operators improves performance. We also introduce an iterative graph neural network, PIGN, that further demonstrates benefits of iterations. Our work aims to enhance the understanding of deep learning by merging insights from numerical analysis, potentially guiding the design of future networks with clearer theoretical underpinnings and improved performance.

Recent AI-based 3D content creation has largely evolved along two paths: feed-forward image-to-3D reconstruction approaches and 3D generative models trained with 2D or 3D supervision. In this work, we show that existing feed-forward reconstruction methods can serve as effective latent encoders for training 3D generative models, thereby bridging these two paradigms. By reusing powerful pre-trained reconstruction models, we avoid computationally expensive encoder network training and obtain rich 3D latent features for generative modeling for free. However, the latent spaces of reconstruction models are not well-suited for generative modeling due to their unstructured nature. To enable flow-based model training on these latent features, we develop post-processing pipelines, including protocols to standardize the features and spatial weighting to concentrate on important regions. We further incorporate a 2D image space perceptual rendering loss to handle the high-dimensional latent spaces. Finally, we propose a multi-stream transformer-based rectified flow architecture to achieve linear scaling and high-quality text-conditioned 3D generation. Our framework leverages the advancements of feed-forward reconstruction models to enhance the scalability of 3D generative modeling, achieving both high computational efficiency and state-of-the-art performance in text-to-3D generation.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching. Our code is available at: https://github.com/daidedou/diffumatch/

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

Generative flow networks (GFlowNets) are a family of algorithms that learn a generative policy to sample discrete objects x with non-negative reward R(x). Learning objectives guarantee the GFlowNet samples x from the target distribution p^*(x) propto R(x) when loss is globally minimized over all states or trajectories, but it is unclear how well they perform with practical limits on training resources. We introduce an efficient evaluation strategy to compare the learned sampling distribution to the target reward distribution. As flows can be underdetermined given training data, we clarify the importance of learned flows to generalization and matching p^*(x) in practice. We investigate how to learn better flows, and propose (i) prioritized replay training of high-reward x, (ii) relative edge flow policy parametrization, and (iii) a novel guided trajectory balance objective, and show how it can solve a substructure credit assignment problem. We substantially improve sample efficiency on biochemical design tasks.

Vision-language-action (VLA) models have demonstrated exceptional performance in natural language-driven perception and control. However, the high computational cost of VLA models poses significant efficiency challenges, particularly for resource-constrained edge platforms in real-world deployments. However, since different stages of VLA (observation, action generation and execution) must proceed sequentially, and wait for the completion of the preceding stage, the system suffers from frequent halting and high latency. To address this, We conduct a systematic analysis to identify the challenges for fast and fluent generation, and propose enabling VLAs with the ability to asynchronously parallelize across VLA stages in a "streaming" manner. First, we eliminate the reliance on action chunking and adopt action flow matching, which learns the trajectory of action flows rather than denoising chunk-wise actions. It overlaps the latency of action generation and execution. Second, we design an action saliency-aware adaptive observation mechanism, thereby overlapping the latency of execution and observation. Without sacrificing performance, StreamingVLA achieves substantial speedup and improves the fluency of execution. It achieves a 2.4 times latency speedup and reduces execution halting by 6.5 times.

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples (e.g., image and text generation), this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.