Related papers: Generative Latent Neural PDE Solver using Flow Mat…

Inspired by recent advances in diffusion models, which are reminiscent of denoising autoencoders, we investigate whether they can acquire discriminative representations for classification via generative pre-training. This paper shows that…

Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…

The slow iterative sampling nature remains a major bottleneck for the practical deployment of diffusion and flow-based generative models. While consistency models (CMs) represent a state-of-the-art distillation-based approach for efficient…

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising…

Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications. Neural PDE solvers offer a promising alternative to classical numerical methods. However, existing approaches typically…

We explore training deep neural network models in conjunction with physics simulations via partial differential equations (PDEs), using the simulated degrees of freedom as latent space for a neural network. In contrast to previous work,…

Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization…

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long,…

Diffusion Probabilistic Models (DPMs) are generative models showing competitive performance in various domains, including image synthesis and 3D point cloud generation. Sampling from pre-trained DPMs involves multiple neural function…

Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremely sparse, which severely limits the applicability of both…

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…

We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…

We propose Speech Enhancement based on Drifting Models (DriftSE), a novel generative framework that formulates denoising as an equilibrium problem. Rather than relying on iterative sampling, DriftSE natively achieves one-step inference by…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

Visual synthesis has recently seen significant leaps in performance, largely due to breakthroughs in generative models. Diffusion models have been a key enabler, as they excel in image diversity. However, this comes at the cost of slow…

Denoising diffusion models produce high-fidelity image samples by capturing the image distribution in a progressive manner while initializing with a simple distribution and compounding the distribution complexity. Although these models have…

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…