Kirill Neklyudov

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

Jungyoon Lee

Joey Bose

Valentin De Bortoli

Arnaud Doucet

Michael M. Bronstein

Siamak Ravanbakhsh

Alexander Tong

Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact sc… (see more)ientific 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

2025-06-19

ArXiv (preprint)

Amortized Sampling with Transferable Normalizing Flows

Charlie B. Tan

Majdi Hassan

Leon Klein

Saifuddin Syed

Michael M. Bronstein

Alexander Tong

2025-06-11

ICML.cc/2025/Workshop/GenBio (spotlight)

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

Jungyoon Lee

Joey Bose

Valentin De Bortoli

Arnaud Doucet

Michael M. Bronstein

Siamak Ravanbakhsh

Alexander Tong

Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact sc… (see more)ientific 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

2025-06-11

ICML.cc/2025/Workshop/GenBio (spotlight)

Self-Refining Training for Amortized Density Functional Theory

Majdi Hassan

Cristian Gabellini

Hatem Helal

Density Functional Theory (DFT) allows for predicting all the chemical and physical properties of molecular systems from first principles by… (see more) finding an approximate solution to the many-body Schr\"odinger equation. However, the cost of these predictions becomes infeasible when increasing the scale of the energy evaluations, e.g., when calculating the ground-state energy for simulating molecular dynamics. Recent works have demonstrated that, for substantially large datasets of molecular conformations, Deep Learning-based models can predict the outputs of the classical DFT solvers by amortizing the corresponding optimization problems. In this paper, we propose a novel method that reduces the dependency of amortized DFT solvers on large pre-collected datasets by introducing a self-refining training strategy. Namely, we propose an efficient method that simultaneously trains a deep-learning model to predict the DFT outputs and samples molecular conformations that are used as training data for the model. We derive our method as a minimization of the variational upper bound on the KL-divergence measuring the discrepancy between the generated samples and the target Boltzmann distribution defined by the ground state energy. To demonstrate the utility of the proposed scheme, we perform an extensive empirical study comparing it with the models trained on the pre-collected datasets. Finally, we open-source our implementation of the proposed algorithm, optimized with asynchronous training and sampling stages, which enables simultaneous sampling and training. Code is available at https://github.com/majhas/self-refining-dft.

2025-06-02

ArXiv (preprint)

Self-Refining Training for Amortized Density Functional Theory

Majdi Hassan

Cristian Gabellini

Hatem Helal

Density Functional Theory (DFT) allows for predicting all the chemical and physical properties of molecular systems from first principles by… (see more) finding an approximate solution to the many-body Schrödinger equation. However, the cost of these predictions becomes infeasible when increasing the scale of the energy evaluations, e.g., when calculating the ground-state energy for simulating molecular dynamics. Recent works have demonstrated that, for substantially large datasets of molecular conformations, Deep Learning-based models can predict the outputs of the classical DFT solvers by amortizing the corresponding optimization problems. In this paper, we propose a novel method that reduces the dependency of amortized DFT solvers on large pre-collected datasets by introducing a self-refining training strategy. Namely, we propose an efficient method that simultaneously trains a deep-learning model to predict the DFT outputs and samples molecular conformations that are used as training data for the model. We derive our method as a minimization of the variational upper bound on the KL-divergence measuring the discrepancy between the generated samples and the target Boltzmann distribution defined by the ground state energy. To demonstrate the utility of the proposed scheme, we perform an extensive empirical study comparing it with the models trained on the pre-collected datasets. Finally, we open-source our implementation of the proposed algorithm, optimized with asynchronous training and sampling stages, which enables simultaneous sampling and training. Code is available at https://github.com/majhas/self-refining-dft.

2025-06-01

arXiv (published)

Scaling Deep Learning Solutions for Transition Path Sampling

Jungyoon Lee

Michael Plainer

Yuanqi Du

Lars Holdijk

Rob Brekelmans

Carla P Gomes

Transition path sampling (TPS) is an important method for studying rare events, such as they happen in chemical reactions or protein folding… (see more). These events occur so infrequently that traditional simulations are often impractical, and even recent machine-learning approaches struggle to address this issue for larger systems. In this paper, we propose using modern deep learning techniques to improve the scalability of TPS methods significantly. We highlight the need for better evaluations in the existing literature and start by formulating TPS as a sampling problem over an unnormalized target density and introduce relevant evaluation metrics to assess the effectiveness of TPS solutions from this perspective. To develop a scalable approach, we explore several design choices, including a problem-informed neural network architecture, simulated annealing, the integration of prior knowledge into the sampling process, and attention mechanisms. Finally, we conduct a comprehensive empirical study and compare these design choices with other recently developed deep-learning methods for rare event sampling.

2025-03-05

ICLR.cc/2025/Workshop/GEM (published)

Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts

Marta Skreta

Viktor Ohanesian

Roberto Bondesan

Alan Aspuru-Guzik

Arnaud Doucet

Rob Brekelmans

Alexander Tong

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling infere… (see more)nce-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional `corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

2025-03-04

ArXiv (preprint)

Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts

Marta Skreta

Viktor Ohanesian

Roberto Bondesan

Alan Aspuru-Guzik

Arnaud Doucet

Rob Brekelmans

Alexander Tong

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling infere… (see more)nce-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

2025-03-04

ArXiv (preprint)

Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts

Marta Skreta

Viktor Ohanesian

Roberto Bondesan

Alan Aspuru-Guzik

Arnaud Doucet

Rob Brekelmans

Alexander Tong

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling infere… (see more)nce-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

2025-03-01

arXiv (published)

Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold

Lazar Atanackovic

Xi Zhang

Brandon Amos

Mathieu Blanchette

Leo J Lee

Yoshua Bengio

Alexander Tong

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynam… (see more)ics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

2025-01-22

ICLR.cc/2025/Conference (poster)

Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints

Lingkai Kong

Yuanqi Du

Wenhao Mu

Valentin De Bortoli

Dongxia Wu

Haorui Wang

Aaron Ferber

Yi-An Ma

Carla P. Gomes

Chao Zhang

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailabl… (see more)e. While numerous studies have addressed the issue of unknown objectives, limited research has focused on scenarios where feasibility constraints are not given explicitly. Overlooking these constraints can lead to spurious solutions that are unrealistic in practice. To deal with such unknown constraints, we propose to perform optimization within the data manifold using diffusion models. To constrain the optimization process to the data manifold, we reformulate the original optimization problem as a sampling problem from the product of the Boltzmann distribution defined by the objective function and the data distribution learned by the diffusion model. Depending on the differentiability of the objective function, we propose two different sampling methods. For differentiable objectives, we propose a two-stage framework that begins with a guided diffusion process for warm-up, followed by a Langevin dynamics stage for further correction. For non-differentiable objectives, we propose an iterative importance sampling strategy using the diffusion model as the proposal distribution. Comprehensive experiments on a synthetic dataset, six real-world black-box optimization datasets, and a multi-objective molecule optimization dataset show that our method achieves better or comparable performance with previous state-of-the-art baselines.

2025-01-01

AISTATS (published)