Sampling and Boltzmann Generators
Developing generative models for sampling from Boltzmann distributions—combining normalizing flows, diffusion, and autoregressive models to generate equilibrium samples of molecular systems.
Boltzmann Generators pair generative models with exact likelihoods and importance sampling to rapidly generate uncorrelated equilibrium samples from molecular systems at thermodynamic equilibrium. This is a hallmark challenge in statistical physics with direct applications to drug discovery and molecular dynamics.

Our group has pioneered several advances in this area: iterated denoising energy matching (iDEM) and progressive inference-time annealing (PITA) for sampling from Boltzmann densities without differentiating the target potential, sequential Boltzmann generators for scalable equilibrium sampling, and amortized sampling with transferable normalizing flows (Prose).
Key Directions
- Diffusion-Based Samplers: Iterated denoising energy matching and progressive inference-time annealing for Boltzmann densities
- Scalable Boltzmann Generators: Sequential and transferable normalizing flows for equilibrium sampling of molecular systems
- Efficient Likelihoods: Few-step accurate likelihoods for continuous flows (FALCON) and forward-only regression training (FORT)
- Autoregressive Approaches: Departing from flow-based paradigms to leverage autoregressive architectures from large language models (ArBG)
- Amortized Sampling: Transferable normalizing flows for amortized sampling across molecular systems (Prose)
People
Selected Publications
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Autoregressive Boltzmann Generators
Danyal Rehman, Charlie B. Tan, Yoshua Bengio, Joey Bose, Alexander Tong
In ICML 2026 (Spotlight)
July 2026
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FALCON: Few-step Accurate Likelihoods for Continuous Flows
Danyal Rehman, Tara Akhound-Sadegh, Artem Gazizov, Yoshua Bengio, Alexander Tong
In ICLR 2026 (Oral)
May 2026
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Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities
Tara Akhound-Sadegh, Jungyoon Lee, Avishek Joey Bose, Valentin De Bortoli, Arnaud Doucet, Michael M. Bronstein, Dominique Beaini, Siamak Ravanbakhsh, Kirill Neklyudov, Alexander Tong
In NeurIPS (spotlight)
December 2025
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Amortized Sampling with Transferable Normalizing Flows
Charlie B. Tan, Majdi Hassan, Leon Klein, Saifuddin Syed, Dominique Beaini, Michael M. Bronstein, Alexander Tong, Kirill Neklyudov
In NeurIPS 2025
December 2025
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FORT: Forward-Only Regression Training of Normalizing Flows
Danyal Rehman, Oscar Davis, Jiarui Lu, Jian Tang, Michael Bronstein, Yoshua Bengio, Alexander Tong, Avishek Joey Bose
ICML GenBio Best Paper Award 2025
July 2025
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Scalable Equilibrium Sampling with Sequential Boltzmann Generators
Charlie B. Tan, Avishek Joey Bose, Chen Lin, Leon Klein, Michael M. Bronstein, Alexander Tong
In ICML 2025
July 2025
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Iterated Denoising Energy Matching for Sampling from Boltzmann Densities
Tara Akhound-Sadegh, Jarrid Rector-Brooks, Avishek Joey Bose, Sarthak Mittal, Pablo Lemos, Cheng-Hao Liu, Marcin Sendera, Siamak Ravanbakhsh, Gauthier Gidel, Yoshua Bengio, Nikolay Malkin, Alexander Tong
In ICML 2024
July 2024