Controlled Generation with Equivariant Variational Flow Matching

TL;DR

This paper introduces a variational flow matching framework for controlled and symmetry-aware generative modeling, especially applied to molecular data, achieving state-of-the-art results in both controlled and uncontrolled generation tasks.

Contribution

It develops a novel variational inference approach within flow matching for controlled generation and establishes equivariant formulations for molecular generation, enabling invariance to key symmetries.

Findings

Achieves state-of-the-art performance in uncontrolled molecular generation.

Outperforms existing models in controlled molecular generation with and without retraining.

Provides a scalable framework connecting flow-based models and Bayesian inference.

Abstract

We derive a controlled generation objective within the framework of Variational Flow Matching (VFM), which casts flow matching as a variational inference problem. We demonstrate that controlled generation can be implemented two ways: (1) by way of end-to-end training of conditional generative models, or (2) as a Bayesian inference problem, enabling post hoc control of unconditional models without retraining. Furthermore, we establish the conditions required for equivariant generation and provide an equivariant formulation of VFM tailored for molecular generation, ensuring invariance to rotations, translations, and permutations. We evaluate our approach on both uncontrolled and controlled molecular generation, achieving state-of-the-art performance on uncontrolled generation and outperforming state-of-the-art models in controlled generation, both with end-to-end training and in the Bayesian inference setting. This work strengthens the connection between flow-based generative modeling and Bayesian inference, offering a scalable and principled framework for constraint-driven and symmetry-aware generation.