Related papers: Functional Adjoint Sampler: Scalable Sampling on I…

We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…

Computational methods for learning to sample from the Boltzmann distribution -- where the target distribution is known only up to an unnormalized energy function -- have advanced significantly recently. Due to the lack of explicit target…

Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…

Recently, there has been significant progress in learning-based diffusion samplers, which aim to sample from a given unnormalized density. Many of these approaches formulate the sampling task as a stochastic optimal control (SOC) problem…

We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…

Accurate characterization of subsurface flow is critical for Carbon Capture and Storage (CCS) but remains challenged by the ill-posed nature of inverse problems with sparse observations. We present Function-space Decoupled Diffusion…

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped…

Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable…

This paper introduces $\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and denoising content only…

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…

Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing…

The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…

We introduce efficient parallel algorithms for sampling from the Gibbs distribution and estimating the partition function of Ising models. These algorithms achieve parallel efficiency, with polylogarithmic depth and polynomial total work,…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…

This paper develops the concept of the Adjacent Deviation Subspace (ADS), a novel framework for reducing infinite-dimensional functional data into finite-dimensional vector or scalar representations while preserving critical information of…

Applications of functional data with large numbers of predictors have grown precipitously in recent years, driven, in part, by rapid advances in genotyping technologies. Given the large numbers of genetic mutations encountered in genetic…

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,…