arXiv subjects

Julius Berner

Publications and source records attributed to Julius Berner.

At least 19 recordsLinked to original sources

arXiv2026

Scaling Reinforcement Learning for Diffusion Models via Velocity Matching

Reward fine-tuning is becoming an important tool for adapting diffusion models to human preferences and task-specific objectives, but existing methods largely inherit policy-gradient machinery from large language models. Unlike autoregressive models, diffusion models do not provide tractable likelihoods for generated samples. As a result, current approaches either construct trajectory likelihoods from stochastic denoising transitions or approximate endpoint likelihoods with evidence lower bound, introducing additional computation and algorithmic complexity. We demonstrate that this likelihood-based machinery is not necessary for effective diffusion reward fine-tuning. We propose reward-based velocity matching (RVM), a simple trajectory-free update that acts directly on the velocity field. RVM reinforces directions associated with high-reward generations, suppresses those with low reward, and involves an optional anchor term controlling drift from a reference velocity. Notably, it provides a general framework that recovers recent fine-tuning methods, including RAM and DiffusionNFT, as special cases. Across various large-scale diffusion models reward fine-tuning tasks, RVM is competitive with or outperforms trajectory-based policy-gradient methods under substantially reduced training cost. We further find that, once the velocity update is simplified, the particular loss variant matters less than reward and anchor design. For video generation, standard preference rewards can favor visually clean but nearly static outputs; introducing a new dynamic-tracking reward that substantially improve motions while improving overall VBench performance. These results suggest that scalable reward fine-tuning for diffusion models is better posed in the native velocity representation than as likelihood-based policy optimization.

cs.CV↗

arXiv2026

Parallel Decoding Distillation for Fast Image and Video Generation

Generation in video diffusion or flow models is computationally expensive due to the slow and iterative sampling process. Current state-of-the-art (SOTA) acceleration methods heavily rely on variational score distillation (VSD) and adversarial losses to distill diffusion models into few-step generators. Albeit achieving high-quality video generation, these training losses are notoriously hard to optimize and suffer from mode collapse, leading to loss of video diversity and lack of motion. In this paper, we introduce Parallel Decoding Distillation (PDD), a simplified and scalable trajectory-based distillation method for fast inference of diffusion and flow matching models. Our architecture and training procedure are compatible with any pre-trained model and support sampling with a varying number of function evaluations (NFE). PDD accelerates generation by predicting multiple denoising steps per network evaluation. Conceptually, it learns a representation of the mean velocity without regressing its derivative using JVPs or finite-difference approximations. Our method achieves SOTA performance with 4-8 NFE on LTX-2.3 Text-to-Video/Audio, Wan 14B Text-to-Video, and Qwen-Image Text-to-Image. Moreover, PDD presents a significant improvement in generated video diversity.

cs.CV↗

arXiv2026

Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling

Diffusion models offer a powerful framework for sampling from complex probability densities by learning to reverse a noising process. A common approach involves solving for the time-reversed stochastic differential equation (SDE), which requires the score function of the evolving sample distribution. The logarithm of this distribution's density is governed by a Hamilton-Jacobi-Bellman (HJB) type partial differential equation (PDE). However, current methods for solving this PDE, such as PINNs or trajectory-based techniques, often suffer from long training times and significant sensitivity to hyperparameter tuning. In this work, we introduce a novel and efficient solver for the underlying HJB equation based on the functional tensor train (FTT) format. The FTT representation leverages latent low-rank structures to efficiently approximate high-dimensional functions, enabling both model compression and rapid computation. By integrating this efficient representation with a backward-in-time iterative scheme derived from backward stochastic differential equations (BSDEs), we develop a fast, robust and accurate sampling method. Our approach overcomes primary bottlenecks of existing techniques, enabling high-fidelity sampling from challenging target distributions with improved efficiency.

stat.ML↗

arXiv2026

Flex-Forcing: Towards a Unified Autoregressive and Bidirectional Video Diffusion Model

Recent progress in large-scale generative models has substantially advanced video generation, yet existing methods remain constrained by a rigid inference paradigm. Bidirectional diffusion models excel at global coherence and visual fidelity but suffer from slow inference, while autoregressive models offer efficient and streaming generation at the cost of long-range consistency and exposure bias. We introduce Flex-Forcing, a unified training and inference framework that enables a video diffusion model to seamlessly operate under both bidirectional and autoregressive generation regimes. The core idea is a flexible chunking mechanism jointly defined over the temporal axis and denoising steps. This design allows the model to (1) perform flexible chunking according to different device budgets, (2) perform bidirectional inference across chunks for global structure planning, while generating frames autoregressively within each chunk for efficient and fine-grained synthesis, and (3) perform any-order, any-timestep autoregressive generation without the strict causal constraint. Extensive experiments on multiple video generation benchmarks demonstrate that Flex-Forcing achieves consistently better video quality, long-video stability than strong baselines with a rigid inference schedule, while offering faster inference.

cs.CV↗

arXiv2026

Towards accurate extreme event likelihoods from diffusion model climate emulators

ML climate model emulators are useful for scenario planning and adaptation, allowing for cost-efficient experimentation. Recently, the diffusion model Climate in a Bottle (cBottle) has been proposed for generation of atmospheric states compatible with boundary conditions of solar position and sea surface temperatures. Crucially, cBottle can be guided to generate extreme events such as Tropical Cyclones (TCs) over locations of interest. Diffusion models such as cBottle work by approximating the probability density of the training data. Here, we show use cases of the probability density estimates of atmospheric states obtained from this climate emulator. Most importantly, these estimates allow us to calculate likelihoods of extreme events under guidance. When guiding the model towards states including TCs, comparing the probability density under the guided and unguided model enables us to quantify how much more likely the guidance has made the TC. We show how these odds ratios allow us to importance-sample from the TC distribution, reducing the standard error of the probability estimate compared to simple Monte Carlo sampling. Furthermore, we discuss results and limitations of the application of model probability densities to extreme event attribution-like experiments. We present these early but encouraging results hoping they will spur more research into probabilistic information that can be gained from diffusion models of the atmosphere.

physics.ao-ph↗

arXiv2026

Variational Flow Maps: Make Some Noise for One-Step Conditional Generation

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and solving inverse problems. We put forth Variational Flow Maps, a framework for conditional sampling that shifts the perspective of conditioning from "guiding a sampling path", to that of "learning the proper initial noise". Specifically, given an observation, we seek to learn a noise adapter model that outputs a noise distribution, so that after mapping to the data space via flow map, the samples respect the observation and data prior. To this end, we develop a principled variational objective that jointly trains the noise adapter and the flow map, improving noise-data alignment, such that sampling from complex data posterior is achieved with a simple adapter. Experiments on various inverse problems show that VFMs produce well-calibrated conditional samples in a single (or few) steps. For ImageNet, VFM attains competitive fidelity while accelerating the sampling by orders of magnitude compared to alternative iterative diffusion/flow models. Code is available at https://github.com/abbasmammadov/VFM

cs.CV↗

arXiv2026

Operator Learning Using Weak Supervision from Walk-on-Spheres

Training neural PDE solvers is often bottlenecked by expensive data generation or unstable physics-informed neural network (PINN) involving challenging optimization landscapes due to higher-order derivatives. To tackle this issue, we propose an alternative approach using Monte Carlo approaches to estimate the solution to the PDE as a stochastic process for weak supervision during training. Leveraging the Walk-on-Spheres method, we introduce a learning scheme called \emph{Walk-on-Spheres Neural Operator (WoS-NO)} which uses weak supervision from WoS to train any given neural operator. We propose to amortize the cost of Monte Carlo walks across the distribution of PDE instances using stochastic representations from the WoS algorithm to generate cheap, noisy, estimates of the PDE solution during training. This is formulated into a data-free physics-informed objective where a neural operator is trained to regress against these weak supervisions, allowing the operator to learn a generalized solution map for an entire family of PDEs. This strategy does not require expensive pre-computed datasets, avoids computing higher-order derivatives for loss functions that are memory-intensive and unstable, and demonstrates zero-shot generalization to novel PDE parameters and domains. Experiments show that for the same number of training steps, our method exhibits up to 8.75$\times$ improvement in $L_2$-error compared to standard physics-informed training schemes, up to 6.31$\times$ improvement in training speed, and reductions of up to 2.97$\times$ in GPU memory consumption. We present the code at https://github.com/neuraloperator/WoS-NO

cs.LG↗

arXiv2026

Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant trade-offs, such as restricting prior distributions or relying on unstable optimization schemes. By generalizing these methods as special forms of fixed-point iterations rooted in Nelson's relation, we develop a new method that addresses these limitations, called Bridge Matching Sampler (BMS). Our approach enables learning a stochastic transport map between arbitrary prior and target distributions with a single, scalable, and stable objective. Furthermore, we introduce a damped variant of this iteration that incorporates a regularization term to mitigate mode collapse and further stabilize training. Empirically, we demonstrate that our method enables sampling at unprecedented scales while preserving mode diversity, achieving state-of-the-art results on complex synthetic densities and high-dimensional molecular benchmarks.

cs.LG↗

arXiv2026

Mode Seeking meets Mean Seeking for Fast Long Video Generation

Scaling video generation from seconds to minutes faces a critical bottleneck: while short-video data is abundant and high-fidelity, coherent long-form data is scarce and limited to narrow domains. To address this, we propose a training paradigm where Mode Seeking meets Mean Seeking, decoupling local fidelity from long-term coherence based on a unified representation via a Decoupled Diffusion Transformer. Our approach utilizes a global Flow Matching head trained via supervised learning on long videos to capture narrative structure, while simultaneously employing a local Distribution Matching head that aligns sliding windows to a frozen short-video teacher via a mode-seeking reverse-KL divergence. This strategy enables the synthesis of minute-scale videos that learns long-range coherence and motions from limited long videos via supervised flow matching, while inheriting local realism by aligning every sliding-window segment of the student to a frozen short-video teacher, resulting in a few-step fast long video generator. Evaluations show that our method effectively closes the fidelity-horizon gap by jointly improving local sharpness, motion and long-range consistency. Project website: https://primecai.github.io/mmm/.

cs.CV↗

arXiv2026

Self-Supervised Learning via Flow-Guided Neural Operator on Time-Series Data

Self-supervised learning (SSL) is a powerful paradigm for learning from unlabeled time-series data. However, popular methods such as masked autoencoders (MAEs) rely on reconstructing inputs from a fixed, predetermined masking ratio. Instead of this static design, we propose treating the corruption level as a new degree of freedom for representation learning, enhancing flexibility and performance. To achieve this, we introduce the Flow-Guided Neural Operator (FGNO), a novel framework combining operator learning with flow matching for SSL training. FGNO learns mappings in functional spaces by using Short-Time Fourier Transform to unify different time resolutions. We extract a rich hierarchy of features by tapping into different network layers and flow times that apply varying strengths of noise to the input data. This enables the extraction of versatile representations, from low-level patterns to high-level global features, using a single model adaptable to specific tasks. Unlike prior generative SSL methods that use noisy inputs during inference, we propose using clean inputs for representation extraction while learning representations with noise; this eliminates randomness and boosts accuracy. We evaluate FGNO across three biomedical domains, where it consistently outperforms established baselines. Our method yields up to 35% AUROC gains in neural signal decoding (BrainTreeBank), 16% RMSE reductions in skin temperature prediction (DREAMT), and over 20% improvement in accuracy and macro-F1 on SleepEDF under low-data regimes. These results highlight FGNO's robustness to data scarcity and its superior capacity to learn expressive representations for diverse time series.

cs.LG↗

arXiv2026

Decoupled Diffusion Sampling for Inverse Problems on Function Spaces

We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics implicitly through joint coefficient-solution modeling, requiring substantial paired supervision. In contrast, our Decoupled Diffusion Inverse Solver (DDIS) employs a decoupled design: an unconditional diffusion learns the coefficient prior, while a neural operator explicitly models the forward PDE for guidance. This decoupling enables superior data efficiency and effective physics-informed learning, while naturally supporting Decoupled Annealing Posterior Sampling (DAPS) to avoid over-smoothing in Diffusion Posterior Sampling (DPS). Theoretically, we prove that DDIS avoids the guidance attenuation failure of joint models when training data is scarce. Empirically, DDIS achieves state-of-the-art performance under sparse observation, improving $l_2$ error by 11% and spectral error by 54% on average; when data is limited to 1%, DDIS maintains accuracy with 40% advantage in $l_2$ error compared to joint models.

cs.LG↗

arXiv2026

Transition Matching Distillation for Fast Video Generation

Large video diffusion and flow models have achieved remarkable success in high-quality video generation, but their use in real-time interactive applications remains limited due to their inefficient multi-step sampling process. In this work, we present Transition Matching Distillation (TMD), a novel framework for distilling video diffusion models into efficient few-step generators. The central idea of TMD is to match the multi-step denoising trajectory of a diffusion model with a few-step probability transition process, where each transition is modeled as a lightweight conditional flow. To enable efficient distillation, we decompose the original diffusion backbone into two components: (1) a main backbone, comprising the majority of early layers, that extracts semantic representations at each outer transition step; and (2) a flow head, consisting of the last few layers, that leverages these representations to perform multiple inner flow updates. Given a pretrained video flow model, we first introduce a flow head to the model, and adapt it into a conditional flow map. We then apply distribution matching distillation to the student model with flow head rollout in each transition step. Extensive experiments on distilling Wan2.1 1.3B and 14B text-to-video models demonstrate that TMD provides a flexible and strong trade-off between generation speed and visual quality. In particular, TMD outperforms existing distilled models under comparable inference costs in terms of visual fidelity and prompt adherence. Project page: https://research.nvidia.com/labs/genair/tmd

cs.CV↗

arXiv2025

There is No VAE: End-to-End Pixel-Space Generative Modeling via Self-Supervised Pre-training

Pixel-space generative models are often more difficult to train and generally underperform compared to their latent-space counterparts, leaving a persistent performance and efficiency gap. In this paper, we introduce a novel two-stage training framework that closes this gap for pixel-space diffusion and consistency models. In the first stage, we pre-train encoders to capture meaningful semantics from clean images while aligning them with points along the same deterministic sampling trajectory, which evolves points from the prior to the data distribution. In the second stage, we integrate the encoder with a randomly initialized decoder and fine-tune the complete model end-to-end for both diffusion and consistency models. Our framework achieves state-of-the-art (SOTA) performance on ImageNet. Specifically, our diffusion model reaches an FID of 1.58 on ImageNet-256 and 2.35 on ImageNet-512 with 75 number of function evaluations (NFE) surpassing prior pixel-space methods and VAE-based counterparts by a large margin in both generation quality and training efficiency. In a direct comparison, our model significantly outperforms DiT while using only around 30\% of its training compute. Furthermore, our consistency model achieves an impressive FID of 8.82 on ImageNet-256, significantly outperforming its latent-space counterparts. This marks the first successful training of a consistency model directly on high-resolution images without relying on pre-trained VAEs or diffusion models. Our codes are available at: \href{https://github.com/AMAP-ML/EPG}{https://github.com/AMAP-ML/EPG}

cs.CV↗

arXiv2025

Physics-Aware Neural Operators for Direct Inversion in 3D Photoacoustic Tomography

Learning physics-constrained inverse operators-rather than post-processing physics-based reconstructions-is a broadly applicable strategy for problems with expensive forward models. We demonstrate this principle in three-dimensional photoacoustic computed tomography (3D PACT), where current systems demand dense transducer arrays and prolonged scans, restricting clinical translation. We introduce PANO (PACT imaging neural operator), an end-to-end physics-aware neural operator-a deep learning architecture that generalizes across input sampling densities without retraining-that directly learns the inverse mapping from raw sensor measurements to a 3D volumetric image. Unlike two-step methods that reconstruct then denoise, PANO performs direct inversion in a single pass, jointly embedding physics and data priors. It employs spherical discrete-continuous convolutions to respect hemispherical sensor geometry and Helmholtz equation constraints to ensure physical consistency. PANO reconstructs high-quality images from both simulated and real data across diverse sparse acquisition settings, achieves real-time inference and outperforms the widely-used UBP algorithm by approximately 33 percentage points in cosine similarity on simulated data and 14 percentage points on real phantom data. These results establish a pathway toward more accessible 3D PACT systems for preclinical research, and motivate future in-vivo validation for clinical translation.

eess.IV↗

arXiv2025

Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference

Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular if the target measure differs substantially from the prior. In this work, we therefore approach the problem by iteratively solving constrained problems incorporating trust regions that aim for approaching the target measure gradually in a systematic way. It turns out that this trust region based strategy can be understood as a geometric annealing from the prior to the target measure, where, however, the incorporated trust regions lead to a principled and educated way of choosing the time steps in the annealing path. We demonstrate in multiple optimal control applications that our novel method can improve performance significantly, including tasks in diffusion-based sampling, transition path sampling, and fine-tuning of diffusion models.

cs.LG↗

arXiv2025

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

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

cs.LG↗

arXiv2025

Guided Diffusion Sampling on Function Spaces with Applications to PDEs

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning. Our method first trains an unconditional, discretization-agnostic denoising model using neural operator architectures. At inference, we refine the samples to satisfy sparse observation data via a gradient-based guidance mechanism. Through rigorous mathematical analysis, we extend Tweedie's formula to infinite-dimensional Banach spaces, providing the theoretical foundation for our posterior sampling approach. Our method (FunDPS) accurately captures posterior distributions in function spaces under minimal supervision and severe data scarcity. Across five PDE tasks with only 3% observation, our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines while reducing sampling steps by 4x. Furthermore, multi-resolution fine-tuning ensures strong cross-resolution generalizability. To the best of our knowledge, this is the first diffusion-based framework to operate independently of discretization, offering a practical and flexible solution for forward and inverse problems in the context of PDEs. Code is available at https://github.com/neuraloperator/FunDPS

cs.LG↗

arXiv2025

Enabling Automatic Differentiation with Mollified Graph Neural Operators

Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these derivatives remains challenging, with spectral and finite difference methods introducing approximation errors due to finite resolution. Here, we propose the mollified graph neural operator ($m$GNO), the first method to leverage automatic differentiation and compute exact gradients on arbitrary geometries. This enhancement enables efficient training on irregular grids and varying geometries while allowing seamless evaluation of physics losses at randomly sampled points for improved generalization. For a PDE example on regular grids, $m$GNO paired with autograd reduced the L2 relative data error by 20x compared to finite differences, although training was slower. It can also solve PDEs on unstructured point clouds seamlessly, using physics losses only, at resolutions vastly lower than those needed for finite differences to be accurate enough. On these unstructured point clouds, $m$GNO leads to errors that are consistently 2 orders of magnitude lower than machine learning baselines (Meta-PDE, which accelerates PINNs) for comparable runtimes, and also delivers speedups from 1 to 3 orders of magnitude compared to the numerical solver for similar accuracy. $m$GNOs can also be used to solve inverse design and shape optimization problems on complex geometries.

cs.LG↗