Underdamped Diffusion Bridges with Applications to Sampling
Keywords: Variational Inference, Sampling, Diffusion Models
TL;DR: We provide a general framework for learning diffusion bridges, including degenerate noise and in particular underdamped versions, which are applied in the context of sampling.
Abstract: 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 previous findings, our framework allows to rigorously show that score-matching in the underdamped case is indeed equivalent to maximizing a lower bound on the likelihood. Motivated by superior convergence properties and compatibility with sophisticated numerical integration schemes of underdamped stochastic processes, we propose *underdamped diffusion bridges*, where a general density evolution is learned rather than prescribed by a fixed noising process. We apply our method to the challenging task of sampling from unnormalized densities without access to samples from the target distribution. Across a diverse range of sampling problems, our approach demonstrates state-of-the-art performance, notably outperforming alternative methods, while requiring significantly fewer discretization steps and almost no hyperparameter tuning.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 12283
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