Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities

• URL: http://arxiv.org/abs/2506.16471v1
• Date: Thu, 19 Jun 2025 17:14:22 GMT
• Title: Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities
• Authors: Tara Akhound-Sadegh, Jungyoon Lee, Avishek Joey Bose, Valentin De Bortoli, Arnaud Doucet, Michael M. Bronstein, Dominique Beaini, Siamak Ravanbakhsh, Kirill Neklyudov, Alexander Tong,
• Abstract summary: We propose Progressive Inference-Time Annealing (PITA) to learn diffusion-based samplers.<n>PITA combines two complementary techniques: Annealing of the Boltzmann distribution and Diffusion smoothing.<n>It enables equilibrium sampling of N-body particle systems, Alanine Dipeptide, and tripeptides in Cartesian coordinates.
• Score: 85.83359661628575
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact scientific applications. A promising approach towards this challenge is the design of amortized samplers that borrow key ideas, such as probability path design, from state-of-the-art generative diffusion models. However, all existing diffusion-based samplers remain unable to draw samples from distributions at the scale of even simple molecular systems. In this paper, we propose Progressive Inference-Time Annealing (PITA), a novel framework to learn diffusion-based samplers that combines two complementary interpolation techniques: I.) Annealing of the Boltzmann distribution and II.) Diffusion smoothing. PITA trains a sequence of diffusion models from high to low temperatures by sequentially training each model at progressively higher temperatures, leveraging engineered easy access to samples of the temperature-annealed target density. In the subsequent step, PITA enables simulating the trained diffusion model to procure training samples at a lower temperature for the next diffusion model through inference-time annealing using a novel Feynman-Kac PDE combined with Sequential Monte Carlo. Empirically, PITA enables, for the first time, equilibrium sampling of N-body particle systems, Alanine Dipeptide, and tripeptides in Cartesian coordinates with dramatically lower energy function evaluations. Code available at: https://github.com/taraak/pita

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