23 accepted papers
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…
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 model…
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…
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. While multi-resolution image training works because higher resolution is largely an interpolation of th…
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 o…
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
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_,…
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…
Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to cor…
Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized sm…
An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed dens…
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.…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices, where the noise only acts in certain dimensions. Extending prev…
Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the inherent complexity and diversity, such as long trajectories, multiple scales and varying dimensions of partial differen…
Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on previous work, we identify these approaches as special cases o…
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, suc…
Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we prop…
We propose Neural Walk-on-Spheres (NWoS), a novel neural PDE solver for the efficient solution of high-dimensional Poisson equations. Leveraging stochastic representations and Walk-on-Spheres methods, we develop novel losses for neural networks based on the recursive solution of Poisson equations on…
Statistical learning theory provides bounds on the necessary number of training samples needed to reach a prescribed accuracy in a learning problem formulated over a given target class. This accuracy is typically measured in terms of a generalization error, that is, an expected value of a given loss…
We investigate the mathematical capabilities of two versions of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel evaluation scheme. In contrast to formal mathematics, where large databases o…
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations based on associated stochastic differential equations (SDEs),…
We present a deep learning algorithm for the numerical solution of parametric families of high-dimensional linear Kolmogorov partial differential equations (PDEs). Our method is based on reformulating the numerical approximation of a whole family of Kolmogorov PDEs as a single statistical learning p…
Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters, the main loss function generally only depends on the realization of the neural network, i.e. the function it computes.…