Alexander Tong

Diffusion language models have emerged as a powerful alternative to autoregressive models, enabling fast inference through flexible and para… (see more)llel generation paths. This flexibility is enabled by new sampling strategies, or planners, that iteratively choose where to denoise along the sequence rather than sampling uniformly at random. However, by modifying reverse paths, planners introduce a mismatch between the uniformly random denoising paths used during training and the planning-based paths used at inference. In this work, we systematically investigate this mismatch and theoretically show that the standard discrete diffusion training evidence lower bound (ELBO) does not accurately describe a denoiser under non-uniform planning. To bridge this gap, we derive a new Planned Evidence Lower Bound (P-ELBO) that directly incorporates planner-based reverse dynamics into the training objective. Building on this, we propose Planner Aware Path Learning (PAPL), a simple and effective modification of the standard masked discrete diffusion loss that aligns training and inference under planned denoisers. Empirically, PAPL delivers consistent improvements across domains, including a 40% relative gain in protein sequence modeling, up to a 4x improvement in MAUVE for text generation, and a 23% relative gain in HumanEval pass@10 for code generation.

2025-09-27

ArXiv (preprint)

Amortized Sampling with Transferable Normalizing Flows

Charlie B. Tan

Majdi Hassan

Leon Klein

Saifuddin Syed

Dominique Beaini

Michael M. Bronstein

Efficient equilibrium sampling of molecular conformations remains a core challenge in computational chemistry and statistical inference. Cla… (see more)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 (preprint)

Amortized Sampling with Transferable Normalizing Flows

Charlie B. Tan

Majdi Hassan

Leon Klein

Saifuddin Syed

Dominique Beaini

Michael M. Bronstein

Efficient equilibrium sampling of molecular conformations remains a core challenge in computational chemistry and statistical inference. Cla… (see more)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 (published)

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

Jungyoon Lee

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… (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

2025-06-20

ArXiv (preprint)

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

Jungyoon Lee

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… (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

Dominique Beaini

Michael M. Bronstein

2025-06-11

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

openreview.net

FORT: Forward-Only Regression Training of Normalizing Flows

Oscar Davis

Michael M. Bronstein

Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to neura… (see more)l dynamical systems that encompass modern large-scale diffusion and flow matching models. Despite the scalability of training, the generation of high-quality samples and their corresponding likelihood under the model requires expensive numerical simulation -- inhibiting adoption in numerous scientific applications such as equilibrium sampling of molecular systems. In this paper, we revisit classical normalizing flows as one-step generative models with exact likelihoods and propose a novel, scalable training objective that does not require computing the expensive change of variable formula used in conventional maximum likelihood training. We propose Forward-Only Regression Training (FORT), a simple

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

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… (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)

openreview.net

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… (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

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

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)

Scalable Equilibrium Sampling with Sequential Boltzmann Generators

Charlie B. Tan

Chen Lin

Leon Klein

Michael M. Bronstein

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators… (see more) tackle this problem by pairing powerful normalizing flows with importance sampling to obtain statistically independent samples under the target distribution. In this paper, we extend the Boltzmann generator framework and introduce Sequential Boltzmann generators (SBG) with two key improvements. The first is a highly efficient non-equivariant Transformer-based normalizing flow operating directly on all-atom Cartesian coordinates. In contrast to equivariant continuous flows of prior methods, we leverage exactly invertible non-equivariant architectures which are highly efficient both during sample generation and likelihood computation. As a result, this unlocks more sophisticated inference strategies beyond standard importance sampling. More precisely, as a second key improvement we perform inference-time scaling of flow samples using annealed Langevin dynamics which transports samples toward the target distribution leading to lower variance (annealed) importance weights which enable higher fidelity resampling with sequential Monte Carlo. SBG achieves state-of-the-art performance w.r.t. all metrics on molecular systems, demonstrating the first equilibrium sampling in Cartesian coordinates of tri, tetra, and hexapeptides that were so far intractable for prior Boltzmann generators.

2025-02-25

ArXiv (preprint)