ICML 2025

Progressive Tempering Sampler with Diffusion
Severi Rissanen * 1 RuiKang OuYang * 2 Jiajun He 2 Wenlin Chen 2 3 Markus Heinonen 1 Arno Solin 1
Jos´e Miguel Hern´andez-Lobato 2
Abstract
Recent research has focused on designing neu-
ral samplers that amortize the process of sam-
pling from unnormalized densities. However, de-
spite significant advancements, they still fall short
of the state-of-the-art MCMC approach, Parallel
Tempering (PT), when it comes to the efficiency
of target evaluations. On the other hand, unlike a
well-trained neural sampler, PT yields only depen-
dent samples and needs to be rerun—at consider-
able computational cost—whenever new samples
are required. To address these weaknesses, we
propose the Progressive Tempering Sampler with
Diffusion (PTSD), which trains diffusion models
sequentially across temperatures, leveraging the
advantages of PT to improve the training of neu-
ral samplers. We also introduce a novel method
to combine high-temperature diffusion models to
generate approximate lower-temperature samples,
which are minimally refined using MCMC and
used to train the next diffusion model. PTSD en-
ables efficient reuse of sample information across
temperature levels while generating well-mixed,
uncorrelated samples. Our method significantly
improves target evaluation efficiency, outperform-
ing diffusion-based neural samplers.
1. Introduction
Sampling from probability distributions is a fundamental
problem in many fields of science, including Bayesian infer-
ence (Gelman et al., 2013; Welling & Teh, 2011), statistical
physics (Von Toussaint, 2011) and molecular simulations
*Equal contribution
1Department of Computer Science,
Aalto University, Finland 2Department of Engineering, Univer-
sity of Cambridge, United Kingdom 3Department of Empir-
ical Inference, Max Planck Institute for Intelligent Systems,
T¨ubingen, Germany. Correspondence to: Severi Rissanen <sev-
eri.rissanen@aalto.fi>, RuiKang OuYang <ro352@cam.ac.uk>,
Jiajun He <jh2383@...