Kirill Neklyudov

Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models

David Layden

Ryan Sweke

Vojtvech Havl'ivcek

Anirban Chowdhury

2025-10-09

ArXiv (prépublication)

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

Marta Skreta

Viktor Ohanesian

Roberto Bondesan

Alan Aspuru-Guzik

Arnaud Doucet

Rob Brekelmans

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling infere… (voir plus)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.

2025-10-06

Proceedings of the 42nd International Conference on Machine Learning (publié)

proceedings.mlr.press

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

Marta Skreta

Viktor Ohanesian

Roberto Bondesan

Alan Aspuru-Guzik

Arnaud Doucet

Rob Brekelmans

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling infere… (voir plus)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.

2025-10-06

Proceedings of the 42nd International Conference on Machine Learning (publié)

Amortized Sampling with Transferable Normalizing Flows

Charlie B. Tan

Leon Klein

Saifuddin Syed

Michael M. Bronstein

Efficient equilibrium sampling of molecular conformations remains a core challenge in computational chemistry and statistical inference. Cla… (voir plus)ssical approaches such as molecular dynamics or Markov chain Monte Carlo inherently lack amortization; the computational cost of sampling must be paid in-full for each system of interest. The widespread success of generative models has inspired interest into overcoming this limitation through learning sampling algorithms. Despite performing on par with conventional methods when trained on a single system, learned samplers have so far demonstrated limited ability to transfer across systems. We prove that deep learning enables the design of scalable and transferable samplers by introducing Prose, a 280 million parameter all-atom transferable normalizing flow trained on a corpus of peptide molecular dynamics trajectories up to 8 residues in length. Prose draws zero-shot uncorrelated proposal samples for arbitrary peptide systems, achieving the previously intractable transferability across sequence length, whilst retaining the efficient likelihood evaluation of normalizing flows. Through extensive empirical evaluation we demonstrate the efficacy of Prose as a proposal for a variety of sampling algorithms, finding a simple importance sampling-based finetuning procedure to achieve superior performance to established methods such as sequential Monte Carlo on unseen tetrapeptides. We open-source the Prose codebase, model weights, and training dataset, to further stimulate research into amortized sampling methods and finetuning objectives.

2025-08-25

ArXiv (prépublication)

Amortized Sampling with Transferable Normalizing Flows

Charlie B. Tan

Leon Klein

Saifuddin Syed

Michael M. Bronstein

Efficient equilibrium sampling of molecular conformations remains a core challenge in computational chemistry and statistical inference. Cla… (voir plus)ssical approaches such as molecular dynamics or Markov chain Monte Carlo inherently lack amortization; the computational cost of sampling must be paid in-full for each system of interest. The widespread success of generative models has inspired interest into overcoming this limitation through learning sampling algorithms. Despite performing on par with conventional methods when trained on a single system, learned samplers have so far demonstrated limited ability to transfer across systems. We prove that deep learning enables the design of scalable and transferable samplers by introducing Prose, a 280 million parameter all-atom transferable normalizing flow trained on a corpus of peptide molecular dynamics trajectories up to 8 residues in length. Prose draws zero-shot uncorrelated proposal samples for arbitrary peptide systems, achieving the previously intractable transferability across sequence length, whilst retaining the efficient likelihood evaluation of normalizing flows. Through extensive empirical evaluation we demonstrate the efficacy of Prose as a proposal for a variety of sampling algorithms, finding a simple importance sampling-based finetuning procedure to achieve superior performance to established methods such as sequential Monte Carlo on unseen tetrapeptides. We open-source the Prose codebase, model weights, and training dataset, to further stimulate research into amortized sampling methods and finetuning objectives.

2025-08-01

arXiv (publié)

Discrete Feynman-Kac Correctors

Alan Aspuru-Guzik

The performance of Large Language Models (LLMs) directly depends on the size of the context that the model was trained on. Despite significa… (voir plus)nt progress in increasing the context size of the current models, some applications remain bottlenecked by the number of processed tokens at inference time. A particular mathematical problem LLMs can be used for is inferring parameters in a statistical model, given data-points as input. Here we make a case demonstrating that discrete diffusion models offer a promising avenue for scaling such parameter prediction tasks, by combining the outputs of the same model evaluated on different parts of the training data. We propose Discrete Fenyman-Kac Correctors --- a framework that allows for controlling the generated distribution of discrete masked diffusion models at inference time. We derive Sequential Monte Carlo (SMC) algorithms that, given a trained discrete diffusion model, sample from its annealed distribution or the product of distributions with different conditions. Notably, our framework does not require any training, finetuning and external reward functions. Finally, we apply our framework to amortized linear regression using LLaDA and demonstrate that it drastically outperforms the standard inference procedure in terms of accuracy and adherence to prompt format.

2025-07-09

ICML.cc/2025/Workshop/AI4MATH (poster)

openreview.net

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

Jungyoon Lee

Joey Bose

Valentin De Bortoli

Arnaud Doucet

Michael M. Bronstein

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

2025-06-20

ArXiv (prépublication)

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

Jungyoon Lee

Joey Bose

Valentin De Bortoli

Arnaud Doucet

Michael M. Bronstein

Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact sc… (voir plus)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 (prépublication)

Amortized Sampling with Transferable Normalizing Flows

Charlie B. Tan

Leon Klein

Saifuddin Syed

Michael M. Bronstein

2025-06-11

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

openreview.net

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

Jungyoon Lee

Joey Bose

Valentin De Bortoli

Arnaud Doucet

Michael M. Bronstein

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

openreview.net

Self-Refining Training for Amortized Density Functional Theory

Cristian Gabellini

Hatem Helal

Density Functional Theory (DFT) allows for predicting all the chemical and physical properties of molecular systems from first principles by… (voir plus) 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 (prépublication)