Daily Papers

Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise (varepsilon) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional settings. However, a formal explanation of why the optimal target depends on the specific properties of the data remains elusive. In this work, we provide a theoretical framework based on a generalized prediction formulation that accommodates arbitrary output targets, of which varepsilon-, v-, and x-prediction are special cases. We derive the analytical relationship between data's geometry and the optimal prediction target, offering a rigorous justification for why x-prediction becomes superior when the ambient dimension significantly exceeds the data's intrinsic dimension. Furthermore, while our theory identifies dimensionality as the governing factor for the optimal prediction target, the intrinsic dimension of manifold-bound data is typically intractable to estimate in practice. To bridge this gap, we propose k-Diff, a framework that employs a data-driven approach to learn the optimal prediction parameter k directly from data, bypassing the need for explicit dimension estimation. Extensive experiments in both latent-space and pixel-space image generation demonstrate that k-Diff consistently outperforms fixed-target baselines across varying architectures and data scales, providing a principled and automated approach to enhancing generative performance.

Modern music producers commonly use MIDI (Musical Instrument Digital Interface) to store their musical compositions. However, MIDI files created with digital software may lack the expressive characteristics of human performances, essentially leaving the velocity parameter - a control for note loudness - undefined, which defaults to a flat value. The task of filling MIDI velocity is termed MIDI velocity prediction, which uses regression models to enhance music expressiveness by adjusting only this parameter. In this paper, we introduce the U-Net, a widely adopted architecture in image colorization, to this task. By conceptualizing MIDI data as images, we adopt window attention and develop a custom loss function to address the sparsity of MIDI-converted images. Current dataset availability restricts our experiments to piano data. Evaluated on the MAESTRO v3 and SMD datasets, our proposed method for filling MIDI velocity outperforms previous approaches in both quantitative metrics and qualitative listening tests.

World models that forecast scene evolution by generating future video frames devote the bulk of their capacity to photometric details, yet the resulting predictions often remain geometrically inconsistent. We present VGGT-World, a geometry world model that side-steps video generation entirely and instead forecasts the temporal evolution of frozen geometry-foundation-model (GFM) features. Concretely, we repurpose the latent tokens of a frozen VGGT as the world state and train a lightweight temporal flow transformer to autoregressively predict their future trajectory. Two technical challenges arise in this high-dimensional (d=1024) feature space: (i) standard velocity-prediction flow matching collapses, and (ii) autoregressive rollout suffers from compounding exposure bias. We address the first with a clean-target (z-prediction) parameterization that yields a substantially higher signal-to-noise ratio, and the second with a two-stage latent flow-forcing curriculum that progressively conditions the model on its own partially denoised rollouts. Experiments on KITTI, Cityscapes, and TartanAir demonstrate that VGGT-World significantly outperforms the strongest baselines in depth forecasting while running 3.6-5 times faster with only 0.43B trainable parameters, establishing frozen GFM features as an effective and efficient predictive state for 3D world modeling.

We introduce the Expanded Groove MIDI dataset (E-GMD), an automatic drum transcription (ADT) dataset that contains 444 hours of audio from 43 drum kits, making it an order of magnitude larger than similar datasets, and the first with human-performed velocity annotations. We use E-GMD to optimize classifiers for use in downstream generation by predicting expressive dynamics (velocity) and show with listening tests that they produce outputs with improved perceptual quality, despite similar results on classification metrics. Via the listening tests, we argue that standard classifier metrics, such as accuracy and F-measure score, are insufficient proxies of performance in downstream tasks because they do not fully align with the perceptual quality of generated outputs.

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.

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.

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

Whole-body loco-manipulation for quadruped robots with arms remains a challenging problem, particularly in achieving multi-task control. To address this, we propose MLM, a reinforcement learning framework driven by both real-world and simulation data. It enables a six-DoF robotic arm-equipped quadruped robot to perform whole-body loco-manipulation for multiple tasks autonomously or under human teleoperation. To address the problem of balancing multiple tasks during the learning of loco-manipulation, we introduce a trajectory library with an adaptive, curriculum-based sampling mechanism. This approach allows the policy to efficiently leverage real-world collected trajectories for learning multi-task loco-manipulation. To address deployment scenarios with only historical observations and to enhance the performance of policy execution across tasks with different spatial ranges, we propose a Trajectory-Velocity Prediction policy network. It predicts unobservable future trajectories and velocities. By leveraging extensive simulation data and curriculum-based rewards, our controller achieves whole-body behaviors in simulation and zero-shot transfer to real-world deployment. Ablation studies in simulation verify the necessity and effectiveness of our approach, while real-world experiments on a Go2 robot with an Airbot robotic arm demonstrate the policy's good performance in multi-task execution.

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.

Vision-Language-Action (VLA) models based on flow matching -- such as pi0, pi0.5, and SmolVLA -- achieve state-of-the-art generalist robotic manipulation, yet their iterative denoising, typically 10 ODE steps, introduces substantial latency: on a modern GPU, denoising alone accounts for 80% of end-to-end inference time. Naively reducing the step count is unreliable, degrading success on most tasks due to the velocity field being uncalibrated for single-step jumps. We present SnapFlow, a plug-and-play self-distillation method that compresses multi-step denoising into a single forward pass (1-NFE) for flow-matching VLAs. SnapFlow mixes standard flow-matching samples with consistency samples whose targets are two-step Euler shortcut velocities computed from the model's own marginal velocity predictions, avoiding the trajectory drift caused by conditional velocities, as we analyze theoretically. A zero-initialized target-time embedding lets the network switch between local velocity estimation and global one-step generation within a single architecture. SnapFlow requires no external teacher, no architecture changes, and trains in ~12h on a single GPU. We validate on two VLA architectures spanning a 6x parameter range, with identical hyperparameters: on pi0.5 (3B) across four LIBERO suites (40 tasks, 400 episodes), SnapFlow achieves 98.75% average success -- matching the 10-step teacher at 97.75% and slightly exceeding it -- with 9.6x denoising speedup and end-to-end latency reduced from 274ms to 83ms; on SmolVLA (500M), it reduces MSE by 8.3% with 3.56x end-to-end acceleration. An action-step sweep on long-horizon tasks reveals that SnapFlow maintains its advantage across execution horizons, achieving 93% at n_act=5 where the baseline reaches only 90%. SnapFlow is orthogonal to layer-distillation and token-pruning approaches, enabling compositional speedups.

The purpose of this study is to present and compare three denoising diffusion probabilistic models (DDPMs) that generate 3D T_1-weighted MRI human brain images. Three DDPMs were trained using 80,675 image volumes from 42,406 subjects spanning 38 publicly available brain MRI datasets. These images had approximately 1 mm isotropic resolution and were manually inspected by three human experts to exclude those with poor quality, field-of-view issues, and excessive pathology. The images were minimally preprocessed to preserve the visual variability of the data. Furthermore, to enable the DDPMs to produce images with natural orientation variations and inhomogeneity, the images were neither registered to a common coordinate system nor bias field corrected. Evaluations included segmentation, Frechet Inception Distance (FID), and qualitative inspection. Regarding results, all three DDPMs generated coherent MR brain volumes. The velocity and flow prediction models achieved lower FIDs than the sample prediction model. However, all three models had higher FIDs compared to real images across multiple cohorts. In a permutation experiment, the generated brain regional volume distributions differed statistically from real data. However, the velocity and flow prediction models had fewer statistically different volume distributions in the thalamus and putamen. In conclusion this work presents and releases the first 3D non-latent diffusion model for brain data without skullstripping or registration. Despite the negative results in statistical testing, the presented DDPMs are capable of generating high-resolution 3D T_1-weighted brain images. All model weights and corresponding inference code are publicly available at https://github.com/piksl-research/medforj .

We verify a recent prediction (Eq. 3.50 in G. L. Eyink, Phys. Rev. X 11, 031054 (2021)) for the drag on an object moving through a fluid. In this prediction the velocity field is decomposed into a nonvortical (potential) and vortical contribution, and so is the associated drag force. In the Josephson-Anderson relation the vortical contribution of the drag force follows from the flux of vorticity traversing the streamlines of the corresponding potential flow. The potential component is directly determined by the plate acceleration and its added mass. The Josephson-Anderson relation is derived from the quantum description of superfluids, but remarkably applies to the classical fluid in our experiment. In our experiment a flat plate is accelerated through water using a robotic arm. This geometry is simple enough to allow analytic potential flow streamlines. The monitored plate position shows an oscillatory component of the acceleration, which adds an additional test of the Josephson-Anderson relation. The instantaneous velocity field is measured using particle image velocimetry. It enables us to evaluate Eq. 3.50 from [1] and compare its prediction to the measured drag force. We find excellent agreement, and, most remarkably find that the added mass contribution to the drag force still stands out after the flow has turned vortical. We finally comment on the requirements on the experimental techniques for evaluating the Josephson-Anderson relation.

This paper tackles the challenge of real-time 3D trajectory prediction for UAVs, which is critical for applications such as aerial surveillance and defense. Existing prediction models that rely primarily on position data struggle with accuracy, especially when UAV movements fall outside the position domain used in training. Our research identifies a gap in utilizing velocity estimates, first-order dynamics, to better capture the dynamics and enhance prediction accuracy and generalizability in any position domain. To bridge this gap, we propose a new trajectory prediction method using Gated Recurrent Units (GRUs) within sequence-based neural networks. Unlike traditional methods that rely on RNNs or transformers, this approach forecasts future velocities and positions based on historical velocity data instead of positions. This is designed to enhance prediction accuracy and scalability, overcoming challenges faced by conventional models in handling complex UAV dynamics. The methodology employs both synthetic and real-world 3D UAV trajectory data, capturing a wide range of flight patterns, speeds, and agility. Synthetic data is generated using the Gazebo simulator and PX4 Autopilot, while real-world data comes from the UZH-FPV and Mid-Air drone racing datasets. The GRU-based models significantly outperform state-of-the-art RNN approaches, with a mean square error (MSE) as low as 2 x 10^-8. Overall, our findings confirm the effectiveness of incorporating velocity data in improving the accuracy of UAV trajectory predictions across both synthetic and real-world scenarios, in and out of position data distributions. Finally, we open-source our 5000 trajectories dataset and a ROS 2 package to facilitate the integration with existing ROS-based UAV systems.

We study reconstructing and predicting 3D fluid appearance and velocity from a single video. Current methods require multi-view videos for fluid reconstruction. We present FluidNexus, a novel framework that bridges video generation and physics simulation to tackle this task. Our key insight is to synthesize multiple novel-view videos as references for reconstruction. FluidNexus consists of two key components: (1) a novel-view video synthesizer that combines frame-wise view synthesis with video diffusion refinement for generating realistic videos, and (2) a physics-integrated particle representation coupling differentiable simulation and rendering to simultaneously facilitate 3D fluid reconstruction and prediction. To evaluate our approach, we collect two new real-world fluid datasets featuring textured backgrounds and object interactions. Our method enables dynamic novel view synthesis, future prediction, and interaction simulation from a single fluid video. Project website: https://yuegao.me/FluidNexus.

Glacial Lake Outburst Floods (GLOFs) are rare but destructive hazards in high mountain regions, yet predictive research is hindered by fragmented and unimodal data. Most prior efforts emphasize post-event mapping, whereas forecasting requires harmonized datasets that combine visual indicators with physical precursors. We present GLOFNet, a multimodal dataset for GLOF monitoring and prediction, focused on the Shisper Glacier in the Karakoram. It integrates three complementary sources: Sentinel-2 multispectral imagery for spatial monitoring, NASA ITS_LIVE velocity products for glacier kinematics, and MODIS Land Surface Temperature records spanning over two decades. Preprocessing included cloud masking, quality filtering, normalization, temporal interpolation, augmentation, and cyclical encoding, followed by harmonization across modalities. Exploratory analysis reveals seasonal glacier velocity cycles, long-term warming of ~0.8 K per decade, and spatial heterogeneity in cryospheric conditions. The resulting dataset, GLOFNet, is publicly available to support future research in glacial hazard prediction. By addressing challenges such as class imbalance, cloud contamination, and coarse resolution, GLOFNet provides a structured foundation for benchmarking multimodal deep learning approaches to rare hazard prediction.

Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to understand the structure and dynamics of these systems. Although networks evolve through time, most existing graph representation learning methods target only static networks. Whereas approaches have been developed for the modeling of dynamic networks, there is a lack of efficient continuous time dynamic graph representation learning methods that can provide accurate network characterization and visualization in low dimensions while explicitly accounting for prominent network characteristics such as homophily and transitivity. In this paper, we propose the Piecewise-Velocity Model (PiVeM) for the representation of continuous-time dynamic networks. It learns dynamic embeddings in which the temporal evolution of nodes is approximated by piecewise linear interpolations based on a latent distance model with piecewise constant node-specific velocities. The model allows for analytically tractable expressions of the associated Poisson process likelihood with scalable inference invariant to the number of events. We further impose a scalable Kronecker structured Gaussian Process prior to the dynamics accounting for community structure, temporal smoothness, and disentangled (uncorrelated) latent embedding dimensions optimally learned to characterize the network dynamics. We show that PiVeM can successfully represent network structure and dynamics in ultra-low two-dimensional spaces. It outperforms relevant state-of-art methods in downstream tasks such as link prediction. In summary, PiVeM enables easily interpretable dynamic network visualizations and characterizations that can further improve our understanding of the intrinsic dynamics of time-evolving networks.

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).

It is well-known that a diverse corpus is critical for training large language models, which are typically constructed from a mixture of various domains. In general, previous efforts resort to sampling training data from different domains with static proportions, as well as adjusting data proportions during training. However, few methods have addressed the complexities of domain-adaptive continual pre-training. To fill this gap, we propose Velocitune, a novel framework dynamically assesses learning velocity and adjusts data proportions accordingly, favoring slower-learning domains while shunning faster-learning ones, which is guided by a scaling law to indicate the desired learning goal for each domain with less associated cost. To evaluate the effectiveness of Velocitune, we conduct experiments in a reasoning-focused dataset with CodeLlama, as well as in a corpus specialised for system command generation with Llama3 and Mistral. Velocitune achieves performance gains in both math and code reasoning tasks and command-line generation benchmarks. Further analysis reveals that key factors driving Velocitune's effectiveness include target loss prediction and data ordering.

Existing video frame interpolation (VFI) methods blindly predict where each object is at a specific timestep t ("time indexing"), which struggles to predict precise object movements. Given two images of a baseball, there are infinitely many possible trajectories: accelerating or decelerating, straight or curved. This often results in blurry frames as the method averages out these possibilities. Instead of forcing the network to learn this complicated time-to-location mapping implicitly together with predicting the frames, we provide the network with an explicit hint on how far the object has traveled between start and end frames, a novel approach termed "distance indexing". This method offers a clearer learning goal for models, reducing the uncertainty tied to object speeds. We further observed that, even with this extra guidance, objects can still be blurry especially when they are equally far from both input frames (i.e., halfway in-between), due to the directional ambiguity in long-range motion. To solve this, we propose an iterative reference-based estimation strategy that breaks down a long-range prediction into several short-range steps. When integrating our plug-and-play strategies into state-of-the-art learning-based models, they exhibit markedly sharper outputs and superior perceptual quality in arbitrary time interpolations, using a uniform distance indexing map in the same format as time indexing. Additionally, distance indexing can be specified pixel-wise, which enables temporal manipulation of each object independently, offering a novel tool for video editing tasks like re-timing.

Although deep learning models have demonstrated remarkable potential in weather prediction, most of them overlook either the physics of the underlying weather evolution or the topology of the Earth's surface. In light of these disadvantages, we develop PASSAT, a novel Physics-ASSisted And Topology-informed deep learning model for weather prediction. PASSAT attributes the weather evolution to two key factors: (i) the advection process that can be characterized by the advection equation and the Navier-Stokes equation; (ii) the Earth-atmosphere interaction that is difficult to both model and calculate. PASSAT also takes the topology of the Earth's surface into consideration, other than simply treating it as a plane. With these considerations, PASSAT numerically solves the advection equation and the Navier-Stokes equation on the spherical manifold, utilizes a spherical graph neural network to capture the Earth-atmosphere interaction, and generates the initial velocity fields that are critical to solving the advection equation from the same spherical graph neural network. In the 5.625^circ-resolution ERA5 data set, PASSAT outperforms both the state-of-the-art deep learning-based weather prediction models and the operational numerical weather prediction model IFS T42. Code and checkpoint are available at https://github.com/Yumenomae/PASSAT_5p625.

Transformer neural operators have recently become an effective approach for surrogate modeling of systems governed by partial differential equations (PDEs). In this paper, we introduce a modified implicit factorized transformer (IFactFormer-m) model which replaces the original chained factorized attention with parallel factorized attention. The IFactFormer-m model successfully performs long-term predictions for turbulent channel flow, whereas the original IFactFormer (IFactFormer-o), Fourier neural operator (FNO), and implicit Fourier neural operator (IFNO) exhibit a poor performance. Turbulent channel flows are simulated by direct numerical simulation using fine grids at friction Reynolds numbers Re_{tau}approx 180,395,590, and filtered to coarse grids for training neural operator. The neural operator takes the current flow field as input and predicts the flow field at the next time step, and long-term prediction is achieved in the posterior through an autoregressive approach. The results show that IFactFormer-m, compared to other neural operators and the traditional large eddy simulation (LES) methods including dynamic Smagorinsky model (DSM) and the wall-adapted local eddy-viscosity (WALE) model, reduces prediction errors in the short term, and achieves stable and accurate long-term prediction of various statistical properties and flow structures, including the energy spectrum, mean streamwise velocity, root mean square (rms) values of fluctuating velocities, Reynolds shear stress, and spatial structures of instantaneous velocity. Moreover, the trained IFactFormer-m is much faster than traditional LES methods. By analyzing the attention kernels, we elucidate the reasons why IFactFormer-m converges faster and achieves a stable and accurate long-term prediction compared to IFactFormer-o. Code and data are available at: https://github.com/huiyu-2002/IFactFormer-m.

This study introduces DrivAerNet, a large-scale high-fidelity CFD dataset of 3D industry-standard car shapes, and RegDGCNN, a dynamic graph convolutional neural network model, both aimed at aerodynamic car design through machine learning. DrivAerNet, with its 4000 detailed 3D car meshes using 0.5 million surface mesh faces and comprehensive aerodynamic performance data comprising of full 3D pressure, velocity fields, and wall-shear stresses, addresses the critical need for extensive datasets to train deep learning models in engineering applications. It is 60\% larger than the previously available largest public dataset of cars, and is the only open-source dataset that also models wheels and underbody. RegDGCNN leverages this large-scale dataset to provide high-precision drag estimates directly from 3D meshes, bypassing traditional limitations such as the need for 2D image rendering or Signed Distance Fields (SDF). By enabling fast drag estimation in seconds, RegDGCNN facilitates rapid aerodynamic assessments, offering a substantial leap towards integrating data-driven methods in automotive design. Together, DrivAerNet and RegDGCNN promise to accelerate the car design process and contribute to the development of more efficient vehicles. To lay the groundwork for future innovations in the field, the dataset and code used in our study are publicly accessible at https://github.com/Mohamedelrefaie/DrivAerNet

In the literature, flows produced by synthetic jets (SJ) have been studied extensively through experiments and numeric simulations. The essential physics of such a complex system has been simplified successfully to Lumped-element models in a wide range of conditions. LE models effectively predict the pressure in the cavity and the velocity in the neck of SJ. But, this does not comprise the complete dynamics of SJ. As soon as the flow starts separating from the neck of the SJ device, vortices and jets form at some distance downstream. These structures are the result of loosening the flow boundaries. Despite such a dramatic change, predictions of LE models remain unverified by measurements of the fully developed jet. We compared predictions of momentum transfer using an LE model with measurements of size and velocity of a fully developed jet/vortex detached from an SJ. Our SJ device operated with air as an active fluid. Comparing measurements and predictions, we found a constant difference for the higher sound pressures. However, the predictions and the measurements follow similar trends. Additionally, we found that the decay rate of the flow regime given by the relationship between the Reynolds and the Strouhal numbers differs significantly when the flow is studied within the neck and downstream the cavity.

The Korteweg-de Vries (KdV) equation serves as a foundational model in nonlinear wave physics, describing the balance between dispersive spreading and nonlinear steepening that gives rise to solitons. This article introduces sangkuriang, an open-source Python library for solving this equation using Fourier pseudo-spectral spatial discretization coupled with adaptive high-order time integration. The implementation leverages just-in-time (JIT) compilation for computational efficiency while maintaining accessibility for instructional purposes. Validation encompasses progressively complex scenarios including isolated soliton propagation, symmetric two-wave configurations, overtaking collisions between waves of differing amplitudes, and three-body interactions. Conservation of the classical invariants is monitored throughout, with deviations remaining small across all test cases. Measured soliton velocities conform closely to theoretical predictions based on the amplitude-velocity relationship characteristic of integrable systems. Complementary diagnostics drawn from information theory and recurrence analysis confirm that computed solutions preserve the regular phase-space structure expected for completely integrable dynamics. The solver outputs data in standard scientific formats compatible with common analysis tools and generates visualizations of spatiotemporal wave evolution. By combining numerical accuracy with practical accessibility on modest computational resources, sangkuriang offers a platform suitable for both classroom demonstrations of nonlinear wave phenomena and exploratory research into soliton dynamics.

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

This study presents an explainable artificial intelligent (XAI) model for predicting pile driving vibrations in Bangkok's soft clay subsoil. A deep neural network was developed using a dataset of 1,018 real-world pile driving measurements, encompassing variations in pile dimensions, hammer characteristics, sensor locations, and vibration measurement axes. The model achieved a mean absolute error (MAE) of 0.276, outperforming traditional empirical methods and other machine learning approaches such as XGBoost and CatBoost. SHapley Additive exPlanations (SHAP) analysis was employed to interpret the model's predictions, revealing complex relationships between input features and peak particle velocity (PPV). Distance from the pile driving location emerged as the most influential factor, followed by hammer weight and pile size. Non-linear relationships and threshold effects were observed, providing new insights into vibration propagation in soft clay. A web-based application was developed to facilitate adoption by practicing engineers, bridging the gap between advanced machine learning techniques and practical engineering applications. This research contributes to the field of geotechnical engineering by offering a more accurate and nuanced approach to predicting pile driving vibrations, with implications for optimizing construction practices and mitigating environmental impacts in urban areas. The model and its source code are publicly available, promoting transparency and reproducibility in geotechnical research.

Despite the increasing availability of high-performance computational resources, Reynolds-Averaged Navier-Stokes (RANS) simulations remain the workhorse for the analysis of turbulent flows in real-world applications. Linear eddy viscosity models (LEVM), the most commonly employed model type, cannot accurately predict complex states of turbulence. This work combines a deep-neural-network-based, nonlinear eddy viscosity model with turbulence realizability constraints as an inductive bias in order to yield improved predictions of the anisotropy tensor. Using visualizations based on the barycentric map, we show that the proposed machine learning method's anisotropy tensor predictions offer a significant improvement over all LEVMs in traditionally challenging cases with surface curvature and flow separation. However, this improved anisotropy tensor does not, in general, yield improved mean-velocity and pressure field predictions in comparison with the best-performing LEVM.

Modern diffusion/flow-based models for image generation typically exhibit two core characteristics: (i) using multi-step sampling, and (ii) operating in a latent space. Recent advances have made encouraging progress on each aspect individually, paving the way toward one-step diffusion/flow without latents. In this work, we take a further step towards this goal and propose "pixel MeanFlow" (pMF). Our core guideline is to formulate the network output space and the loss space separately. The network target is designed to be on a presumed low-dimensional image manifold (i.e., x-prediction), while the loss is defined via MeanFlow in the velocity space. We introduce a simple transformation between the image manifold and the average velocity field. In experiments, pMF achieves strong results for one-step latent-free generation on ImageNet at 256x256 resolution (2.22 FID) and 512x512 resolution (2.48 FID), filling a key missing piece in this regime. We hope that our study will further advance the boundaries of diffusion/flow-based generative models.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

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.

Few-step diffusion or flow-based generative models typically distill a velocity-predicting teacher into a student that predicts a shortcut towards denoised data. This format mismatch has led to complex distillation procedures that often suffer from a quality-diversity trade-off. To address this, we propose policy-based flow models (pi-Flow). pi-Flow modifies the output layer of a student flow model to predict a network-free policy at one timestep. The policy then produces dynamic flow velocities at future substeps with negligible overhead, enabling fast and accurate ODE integration on these substeps without extra network evaluations. To match the policy's ODE trajectory to the teacher's, we introduce a novel imitation distillation approach, which matches the policy's velocity to the teacher's along the policy's trajectory using a standard ell_2 flow matching loss. By simply mimicking the teacher's behavior, pi-Flow enables stable and scalable training and avoids the quality-diversity trade-off. On ImageNet 256^2, it attains a 1-NFE FID of 2.85, outperforming MeanFlow of the same DiT architecture. On FLUX.1-12B and Qwen-Image-20B at 4 NFEs, pi-Flow achieves substantially better diversity than state-of-the-art few-step methods, while maintaining teacher-level quality.

Consistency-based generative models like Shortcut and MeanFlow achieve impressive results via a target-aware design for solving the Probability Flow ODE (PF-ODE). Typically, such methods introduce a target time r alongside the current time t to modulate outputs between a local multi-step derivative (r = t) and a global few-step integral (r = 0). However, the conventional "one input, one output" paradigm enforces a partition of the training budget, often allocating a significant portion (e.g., 75% in MeanFlow) solely to the multi-step objective for stability. This separation forces a trade-off: allocating sufficient samples to the multi-step objective leaves the few-step generation undertrained, which harms convergence and limits scalability. To this end, we propose Duality Models (DuMo) via a "one input, dual output" paradigm. Using a shared backbone with dual heads, DuMo simultaneously predicts velocity v_t and flow-map u_t from a single input x_t. This applies geometric constraints from the multi-step objective to every sample, bounding the few-step estimation without separating training objectives, thereby significantly improving stability and efficiency. On ImageNet 256 times 256, a 679M Diffusion Transformer with SD-VAE achieves a state-of-the-art (SOTA) FID of 1.79 in just 2 steps. Code is available at: https://github.com/LINs-lab/DuMo

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains sim 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

The study of high-speed rotating matter is a crucial research topic in physics due to the emergence of novel phenomena. In this paper, we combined cranking covariant density functional theory (CDFT) with a similar renormalization group approach to decompose the Hamiltonian from the cranking CDFT into different Hermit components, including the non-relativistic term, the dynamical term, the spin-orbit coupling, and the Darwin term. Especially, we obtained the rotational term, the term relating to Zeeman effect-like, and the spin-rotation coupling due to consideration of rotation and spatial component of vector potential. By exploring these operators, we aim to identify novel phenomena that may occur in rotating nuclei. Signature splitting, Zeeman effect-like, spin-rotation coupling, and spin current are among the potential novelties that may arise in rotating nuclei. Additionally, we investigated the observability of these phenomena and their dependence on various factors such as nuclear deformation, rotational angular velocity, and strength of magnetic field.

Information seeking users often pose questions with false presuppositions, especially when asking about unfamiliar topics. Most existing question answering (QA) datasets, in contrast, assume all questions have well defined answers. We introduce CREPE, a QA dataset containing a natural distribution of presupposition failures from online information-seeking forums. We find that 25% of questions contain false presuppositions, and provide annotations for these presuppositions and their corrections. Through extensive baseline experiments, we show that adaptations of existing open-domain QA models can find presuppositions moderately well, but struggle when predicting whether a presupposition is factually correct. This is in large part due to difficulty in retrieving relevant evidence passages from a large text corpus. CREPE provides a benchmark to study question answering in the wild, and our analyses provide avenues for future work in better modeling and further studying the task.

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

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.

Building on the success of diffusion models in visual generation, flow-based models reemerge as another prominent family of generative models that have achieved competitive or better performance in terms of both visual quality and inference speed. By learning the velocity field through flow-matching, flow-based models tend to produce a straighter sampling trajectory, which is advantageous during the sampling process. However, unlike diffusion models for which fast samplers are well-developed, efficient sampling of flow-based generative models has been rarely explored. In this paper, we propose a framework called FlowTurbo to accelerate the sampling of flow-based models while still enhancing the sampling quality. Our primary observation is that the velocity predictor's outputs in the flow-based models will become stable during the sampling, enabling the estimation of velocity via a lightweight velocity refiner. Additionally, we introduce several techniques including a pseudo corrector and sample-aware compilation to further reduce inference time. Since FlowTurbo does not change the multi-step sampling paradigm, it can be effectively applied for various tasks such as image editing, inpainting, etc. By integrating FlowTurbo into different flow-based models, we obtain an acceleration ratio of 53.1%sim58.3% on class-conditional generation and 29.8%sim38.5% on text-to-image generation. Notably, FlowTurbo reaches an FID of 2.12 on ImageNet with 100 (ms / img) and FID of 3.93 with 38 (ms / img), achieving the real-time image generation and establishing the new state-of-the-art. Code is available at https://github.com/shiml20/FlowTurbo.

We present Generative Anchored Fields (GAF), a generative model that learns independent endpoint predictors, J (noise) and K (data), from any point on a linear bridge. Unlike existing approaches that use a single trajectory or score predictor, GAF is trained to recover the bridge endpoints directly via coordinate learning. The velocity field v=K-J emerges from their time-conditioned disagreement. This factorization enables Transport Algebra: algebraic operations on multiple J/K heads for compositional control. With class-specific K_n heads, GAF defines directed transport maps between a shared base noise distribution and multiple data domains, allowing controllable interpolation, multi-class composition, and semantic editing. This is achieved either directly on the predicted data coordinates (K) using Iterative Endpoint Refinement (IER), a novel sampler that achieves high-quality generation in 5-8 steps, or on the emergent velocity field (v). We achieve strong sample quality (FID 7.51 on ImageNet 256times256 and 7.27 on CelebA-HQ 256times 256, without classifier-free guidance) while treating compositional generation as an architectural primitive. Code available at https://github.com/IDLabMedia/GAF.

Diffusion models have achieved impressive generative quality across modalities like 2D images, videos, and 3D shapes, but their inference remains computationally expensive due to the iterative denoising process. While recent caching-based methods effectively reuse redundant computations to speed up 2D and video generation, directly applying these techniques to 3D diffusion models can severely disrupt geometric consistency. In 3D synthesis, even minor numerical errors in cached latent features accumulate, causing structural artifacts and topological inconsistencies. To overcome this limitation, we propose Fast3Dcache, a training-free geometry-aware caching framework that accelerates 3D diffusion inference while preserving geometric fidelity. Our method introduces a Predictive Caching Scheduler Constraint (PCSC) to dynamically determine cache quotas according to voxel stabilization patterns and a Spatiotemporal Stability Criterion (SSC) to select stable features for reuse based on velocity magnitude and acceleration criterion. Comprehensive experiments show that Fast3Dcache accelerates inference significantly, achieving up to a 27.12% speed-up and a 54.8% reduction in FLOPs, with minimal degradation in geometric quality as measured by Chamfer Distance (2.48%) and F-Score (1.95%).

Optimizing large-scale machine learning systems, such as recommendation models for global video platforms, requires navigating a massive hyperparameter search space and, more critically, designing sophisticated optimizers, architectures, and reward functions to capture nuanced user behaviors. Achieving substantial improvements in these areas is a non-trivial task, traditionally relying on extensive manual iterations to test new hypotheses. We propose a self-evolving system that leverages Large Language Models (LLMs), specifically those from Google's Gemini family, to autonomously generate, train, and deploy high-performing, complex model changes within an end-to-end automated workflow. The self-evolving system is comprised of an Offline Agent (Inner Loop) that performs high-throughput hypothesis generation using proxy metrics, and an Online Agent (Outer Loop) that validates candidates against delayed north star business metrics in live production. Our agents act as specialized Machine Learning Engineers (MLEs): they exhibit deep reasoning capabilities, discovering novel improvements in optimization algorithms and model architecture, and formulating innovative reward functions that target long-term user engagement. The effectiveness of this approach is demonstrated through several successful production launches at YouTube, confirming that autonomous, LLM-driven evolution can surpass traditional engineering workflows in both development velocity and model performance.