The paper investigates training diffusion models to sample from distributions defined by unnormalized densities or energy functions. It benchmarks various diffusion-structured inference techniques, including simulation-based variational methods and off-policy approaches such as continuous generative flow networks, highlighting their relative strengths and challenging some prior claims. Additionally, the authors introduce a new exploration strategy for off-policy methods that employs local search in the target space with a replay buffer, demonstrating improved sample quality across multiple target distributions.
By Marcin Sendera, Minsu Kim, Sarthak Mittal, Pablo Lemos, Luca Scimeca, Jarrid Rector-Brooks, Alexandre Adam, Yoshua Bengio, Esmeralda S. Whitammer
arXiv:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.
By Caroline Tatsuoka, Minglei Yang, Dongbin Xiu, Guannan Zhang
arXiv:2502. 04646v2 Announce Type: replace-cross Abstract: Weighted sampling -- sampling from a probability density function (PDF) proportional to the product of a base PDF and a weight function -- is a fundamental technique with wide-ranging applications in variance reduction, biased sampling, data augmentation, and more.
By Heasung Kim, Taekyun Lee, Hyeji Kim, Gustavo de Veciana
arXiv:2608. 08644v1 Announce Type: new Abstract: We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution.
By Tiago da Silva, Esmeralda S. Whitammer, Salem Lahlou
The paper introduces block‑triangular joint drifting, a method that applies a projected drift field to the joint distribution of consecutive states, enabling one‑step generative surrogate models for stochastic transition dynamics. This architecture preserves the current‑state marginal while directly sampling the conditional distribution of next states, allowing stochastic trajectories to be generated with a single model evaluation per time step. Experiments show that the approach achieves accurate marginal and trajectory‑dependent statistics with favorable accuracy‑cost tradeoffs compared to deterministic, diffusion, flow, and distillation‑based generative surrogates.
By Nicholas Geissler, Shreya Jha, Ricardo Baptista, Benjamin Peherstorfer
We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution. Notably, recent studies have shown that this problem can be efficiently solved by learning a deterministic Markov Decision Process (MDP) that progressively builds each object in proportion to the posterior.
The paper introduces a two-step Metropolis–Hastings algorithm designed to efficiently sample from Bayesian empirical likelihood (BayesEL) posterior distributions, addressing challenges posed by the complex, often non‑convex support of empirical likelihood. The method leverages current parameter values and estimating equations to propose new values for remaining parameters, making it suitable for problems with discontinuous estimating equations such as simultaneous quantile regression. Additionally, the approach extends naturally to BayesEL model selection via reversible‑jump MCMC, and the authors demonstrate its utility through several real‑life applications.
By Sanjay Chaudhuri, Teng Yin, Snehashis Chakraborty, Rupsa Roy
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
By Jinyuan Chang, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang, Cheng Yuan
Bernoulli Flow Models (BFM) introduce a continuous global Bernoulli probability flow path for binary data generation, replacing sequential one‑step Markov diffusion chains. By deriving analytical closed‑form posterior transitions over arbitrary time intervals, BFM eliminates the need for approximating multi‑step likelihoods and allows inference with far fewer function evaluations while maintaining sample quality. Experiments demonstrate that a BFM trained with 256 steps achieves an FID of 9.22 on LSUN Churches 256×256 using only 16 sampling steps, outperforming state‑of‑the‑art discrete baselines and remaining competitive under full‑step inference.
By Hao Mo, Liying Yang, Shumin Yao, Xinxing Yu, Ajian Liu, Xudong Mao, Yanyan Liang
arXiv:2609.40024v1 Announce Type: new
Abstract: We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a direc...
By Daniel Habermann, Andreas Bulling, Stefan T. Radev, Paul-Christian B\"urkner
arXiv:2606. 14235v1 Announce Type: new Abstract: Variational Inference (VI) is a fundamental inference technique in Bayesian machine learning for approximating complex posterior distributions.
By Jian Xu, Shigui Li, Wei Chen, Jiacheng Li, Zhiqi Lin, Delu Zeng, Xinghao Ding, John Paisley, Qibin Zhao