Related papers: Diffusion Path Samplers via Sequential Monte Carlo
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
Training neural samplers directly from unnormalized densities without access to target distribution samples presents a significant challenge. A critical desideratum in these settings is achieving comprehensive mode coverage, ensuring the…
This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…
This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate…
Annealing-based neural samplers seek to amortize sampling from unnormalized distributions by training neural networks to transport a family of densities interpolating from source to target. A crucial design choice in the training phase of…
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…
Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling --…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…
This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target…
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…
We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each…
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…
Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
In this work we study the diffusion annealed Langevin dynamics, a score-based diffusion process recently introduced in the theory of generative models and which is an alternative to the classical overdamped Langevin diffusion. Our goal is…