Molecular conformer generation is a fundamental task in computational chemistry. Several machine learning approaches have been developed, but none have outperformed state-of-the-art cheminformatics methods. We propose torsional diffusion, a novel diffusion framework that operates on the space of torsion angles via a diffusion process on the hypertorus and an extrinsic-to-intrinsic score model. On a standard benchmark of drug-like molecules, torsional diffusion generates superior conformer ensembles compared to machine learning and cheminformatics methods in terms of both RMSD and chemical properties, and is orders of magnitude faster than previous diffusion-based models. Moreover, our model provides exact likelihoods, which we employ to build the first generalizable Boltzmann generator.

Low-energy molecular conformers generation (MCG) is a foundational yet challenging problem in drug discovery. Denoising-based methods include diffusion and flow-matching methods that learn mappings from a simple base distribution to the molecular conformer distribution. However, these approaches often suffer from error accumulation during sampling, especially in the low SNR steps, which are hard to train. To address these challenges, we propose a flow-matching refiner for the MCG task. The proposed method initializes sampling from mixed-quality outputs produced by upstream denoising models and reschedules the noise scale to bypass the low-SNR phase, thereby improving sample quality. On the GEOM-QM9 and GEOM-Drugs benchmark datasets, the generator-refiner pipeline improves quality with fewer total denoising steps while preserving diversity.

Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Our approach results in a straightforwardand scalable method that directly operates on all-atom coordinates with minimalassumptions. With the advantages of equivariance and flow matching, ET-Flowsignificantly increases the precision and physical validity of the generated con-formers, while being a lighter model and faster at inference.

Diffusion models are powerful tools for capturing complex distributions, but modeling data with inherent symmetries, such as molecular structures, remains challenging. Equivariant denoisers are commonly used to address this, but they introduce architectural complexity and optimization challenges, including noisy gradients and convergence issues. We propose a novel approach that enforces equivariance through a symmetrized loss function, which applies a time-dependent weighted averaging operation over group actions to the model's prediction target. This ensures equivariance without explicit architectural constraints and reduces gradient variance, leading to more stable and efficient optimization. Our method uses Monte Carlo sampling to estimate the average, incurring minimal computational overhead. We provide theoretical guarantees of equivariance for the minimizer of our loss function and demonstrate its effectiveness on synthetic datasets and the molecular conformation generation task using the GEOM-QM9 dataset. Experiments show improved sample quality compared to existing methods, highlighting the potential of our approach to enhance the scalability and practicality of equivariant diffusion models in generative tasks.

Molecular conformer generation is a fundamental task in computational chemistry. Several machine learning approaches have been developed, but none have outperformed state-of-the-art cheminformatics methods. We propose torsional diffusion, a novel diffusion framework that operates on the space of torsion angles via a diffusion process on the hypertorus and an extrinsic-to-intrinsic score model. On a standard benchmark of drug-like molecules, torsional diffusion generates superior conformer ensembles compared to machine learning and cheminformatics methods in terms of both RMSD and chemical properties, and is orders of magnitude faster than previous diffusion-based models. Moreover, our model provides exact likelihoods, which we employ to build the first generalizable Boltzmann generator.

Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Existing state-of-the-art approaches either resort to large scale transformer-based models that diffuse over conformer fields, or use computationally expensive methods to generate initial structures and diffuse over torsion angles. In this work, we introduce Equivariant Transformer Flow (ET-Flow). We showcase that a well-designed flow matching approach with equivariance and harmonic prior alleviates the need for complex internal geometry calculations and large architectures, contrary to the prevailing methods in the field. Our approach results in a straightforward and scalable method that directly operates on all-atom coordinates with minimal assumptions. With the advantages of equivariance and flow matching, ET-Flow significantly increases the precision and physical validity of the generated conformers, while being a lighter model and faster at inference. Code is available https://github.com/shenoynikhil/ETFlow.

In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost that is orthogonal to sampling time. We tackle the question of how to improve diversity and sample efficiency by moving beyond the common assumption of independent samples. We propose particle guidance, an extension of diffusion-based generative sampling where a joint-particle time-evolving potential enforces diversity. We analyze theoretically the joint distribution that particle guidance generates, how to learn a potential that achieves optimal diversity, and the connections with methods in other disciplines. Empirically, we test the framework both in the setting of conditional image generation, where we are able to increase diversity without affecting quality, and molecular conformer generation, where we reduce the state-of-the-art median error by 13% on average. Deep generative modeling has become pervasive in many computational tasks across computer vision, natural language processing, physical sciences, and beyond. In many applications, these models are used to take a number of representative samples of some distribution of interest like Van Gogh's style paintings or the 3D conformers of a small molecule. Although independent samples drawn from a distribution will perfectly represent it in the limit of infinite samples, for a finite number, this may not be the optimal strategy. Therefore, while deep learning methods have so far largely focused on the task of taking independent identically distributed (I.I.D.) samples from some distribution, this paper examines how one can use deep generative models to take a finite number of samples that can better represent the distribution of interest. In other fields where finite-samples approximations are critical, researchers have developed various techniques to tackle this challenge.