TY - CHAP A1 - Blessing, Denis A1 - Berner, Julius A1 - Richter, Lorenz A1 - Neumann, Gerhard T1 - Underdamped Diffusion Bridges with Applications to Sampling T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - 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 \emph{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 no hyperparameter tuning. Y1 - 2025 UR - https://openreview.net/attachment?id=Q1QTxFm0Is&name=pdf ER - TY - CHAP A1 - Chen, Junhua A1 - Richter, Lorenz A1 - Berner, Julius A1 - Blessing, Denis A1 - Neumann, Gerhard A1 - Anandkumar, Anima T1 - Sequential Controlled Langevin Diffusions T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - 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 densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers. Y1 - 2025 UR - https://openreview.net/pdf?id=dImD2sgy86 ER -