Discrete diffusion models have recently emerged as a promising alternative to the autoregressive approach for generating discrete sequences.… (see more) Sample generation via gradual denoising or demasking processes allows them to capture hierarchical non-sequential interdependencies in the data. These custom processes, however, do not assume a flexible control over the distribution of generated samples. We propose Discrete Feynman-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, control the temperature of the sampled distribution (i.e. perform annealing), sample from the product of marginals of several diffusion processes (e.g. differently conditioned processes), and sample from the product of the marginal with an external reward function, producing likely samples from the target distribution that also have high reward. Notably, our framework does not require any training of additional models or fine-tuning of the original model. We illustrate the utility of our framework in several applications including: efficient sampling from the annealed Boltzmann distribution of the Ising model, improving the performance of language models for code generation and amortized learning, as well as reward-tilted protein sequence generation.

2025-07-08

AI4MATH @ International Conference on Machine Learning (poster)

doi.org

openreview.net

Self-Refining Training for Amortized Density Functional Theory

Majdi Hassan

Cristian Gabellini

Hatem Helal

Dominique Beaini

Kirill Neklyudov

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 (preprint)

doi.org

arxiv.org

Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints

Lingkai Kong

Yuanqi Du

Wenhao Mu

Kirill Neklyudov

Valentin De Bortoli

Haorui Wang

Dongxia Wu

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.

2025-04-22

Proceedings of The 28th International Conference on Artificial Intelligence and Statistics (published)

doi.org

proceedings.mlr.press

The Superposition of Diffusion Models Using the Itô Density Estimator

Marta Skreta

Lazar Atanackovic

Avishek Joey Bose

Alexander Tong

Kirill Neklyudov

The Cambrian explosion of easily accessible pre-trained diffusion models suggests a demand for methods that combine multiple different pre-t… (see more)rained diffusion models without incurring the significant computational burden of re-training a larger combined model. In this paper, we cast the problem of combining multiple pre-trained diffusion models at the generation stage under a novel proposed framework termed superposition. Theoretically, we derive superposition from rigorous first principles stemming from the celebrated continuity equation and design two novel algorithms tailor-made for combining diffusion models in SuperDiff. SuperDiff leverages a new scalable Itô density estimator for the log likelihood of the diffusion SDE which incurs no additional overhead compared to the well-known Hutchinson's estimator needed for divergence calculations. We demonstrate that SuperDiff is scalable to large pre-trained diffusion models as superposition is performed solely through composition during inference, and also enjoys painless implementation as it combines different pre-trained vector fields through an automated re-weighting scheme. Notably, we show that SuperDiff is efficient during inference time, and mimics traditional composition operators such as the logical OR and the logical AND. We empirically demonstrate the utility of using SuperDiff for generating more diverse images on CIFAR-10, more faithful prompt conditioned image editing using Stable Diffusion, as well as improved conditional molecule generation and unconditional de novo structure design of proteins. https://github.com/necludov/super-diffusion

2025-04-22

International Conference on Learning Representations (Accept (Spotlight))

doi.org

openreview.net

Scaling Deep Learning Solutions for Transition Path Sampling

Jungyoon Lee

Michael Plainer

Yuanqi Du

Lars Holdijk

Rob Brekelmans

Carla P Gomes

Dominique Beaini

Kirill Neklyudov

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.

2025-03-04

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

openreview.net

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

Kirill Neklyudov

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 depend on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrate 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 the prediction of individual treatment responses on a large-scale multi-patient single-cell drug screen dataset.

2025-01-21

International Conference on Learning Representations (poster)

doi.org

openreview.net

Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling

Yuanqi Du

Michael Plainer

Rob Brekelmans

Chenru Duan

Frank Noé

Carla P. Gomes

Alán Aspuru-Guzik

Kirill Neklyudov

Rare event sampling in dynamical systems is a fundamental problem arising in the natural sciences, which poses significant computational cha… (see more)llenges due to an exponentially large space of trajectories. For settings where the dynamical system of interest follows a Brownian motion with known drift, the question of conditioning the process to reach a given endpoint or desired rare event is definitively answered by Doob's h-transform. However, the naive estimation of this transform is infeasible, as it requires simulating sufficiently many forward trajectories to estimate rare event probabilities. In this work, we propose a variational formulation of Doob's h-transform as an optimization problem over trajectories between a given initial point and the desired ending point. To solve this optimization, we propose a simulation-free training objective with a model parameterization that imposes the desired boundary conditions by design. Our approach significantly reduces the search space over trajectories and avoids expensive trajectory simulation and inefficient importance sampling estimators which are required in existing methods. We demonstrate the ability of our method to find feasible transition paths on real-world molecular simulation and protein folding tasks.

2024-12-10

Conference on Neural Information Processing Systems (Accept (spotlight))

doi.org

openreview.net

A Computational Framework for Solving Wasserstein Lagrangian Flows

Kirill Neklyudov

Rob Brekelmans

Alexander Tong

Lazar Atanackovic

Qiang Liu

Alireza Makhzani

The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and … (see more)the regularization of density paths (potential energy). These combinations yield different variational problems (Lagrangians), encompassing many variations of the optimal transport problem such as the Schrödinger bridge, unbalanced optimal transport, and optimal transport with physical constraints, among others. In general, the optimal density path is unknown, and solving these variational problems can be computationally challenging. We propose a novel deep learning based framework approaching all of these problems from a unified perspective. Leveraging the dual formulation of the Lagrangians, our method does not require simulating or backpropagating through the trajectories of the learned dynamics, and does not need access to optimal couplings. We showcase the versatility of the proposed framework by outperforming previous approaches for the single-cell trajectory inference, where incorporating prior knowledge into the dynamics is crucial for correct predictions.

2024-07-22

International Conference on Machine Learning (Accept (Poster))

doi.org

proceedings.mlr.press

Structured Inverse-Free Natural Gradient Descent: Memory-Efficient & Numerically-Stable KFAC

Wu Lin

Felix Dangel

Runa Eschenhagen

Kirill Neklyudov

Agustinus Kristiadi

Richard E. Turner

Alireza Makhzani

Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their precondition… (see more)ing Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such methods unpopular for modern mixed-precision training. We address them by (i) formulating an inverse-free KFAC update and (ii) imposing structures in the Kronecker factors, resulting in structured inverse-free natural gradient descent (SINGD). On modern neural networks, we show that SINGD is memory-efficient and numerically robust, in contrast to KFAC, and often outperforms AdamW even in half precision. Our work closes a gap between first- and second-order methods in modern low-precision training.

2024-07-07

Proceedings of the 41st International Conference on Machine Learning (published)

proceedings.mlr.press

Efficient Evolutionary Search Over Chemical Space with Large Language Models

Haorui Wang

Marta Skreta

Cher Tian Ser

Wenhao Gao

Lingkai Kong

Felix Streith-Kalthoff

Chenru Duan

Yuchen Zhuang

Yue Yu

Yanqiao Zhu 0001

Yuanqi Du

Alán Aspuru-Guzik

Kirill Neklyudov

Chao Zhang

Molecular discovery, when formulated as an optimization problem, presents significant computational challenges because optimization objectiv… (see more)es can be non-differentiable. Evolutionary Algorithms (EAs), often used to optimize black-box objectives in molecular discovery, traverse chemical space by performing random mutations and crossovers, leading to a large number of expensive objective evaluations. In this work, we ameliorate this shortcoming by incorporating chemistry-aware Large Language Models (LLMs) into EAs. Namely, we redesign crossover and mutation operations in EAs using LLMs trained on large corpora of chemical information. We perform extensive empirical studies on both commercial and open-source models on multiple tasks involving property optimization, molecular rediscovery, and structure-based drug design, demonstrating that the joint usage of LLMs with EAs yields superior performance over all baseline models across single- and multi-objective settings. We demonstrate that our algorithm improves both the quality of the final solution and convergence speed, thereby reducing the number of required objective evaluations. Our code is available at http://github.com/zoom-wang112358/MOLLEO

2024-06-22

ArXiv (preprint)

doi.org

arxiv.org

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