Controlled Generation with Equivariant Variational Flow Matching

2025-06-23

AI Summary

This work addresses the challenges of controllable generation and geometric symmetry modeling in flow-based molecular generative models. We propose Equivariant Variational Flow Matching (EVFM), a novel framework that formulates flow matching as a variational inference problem. EVFM is the first method to guarantee strict equivariance under 3D rotations, translations, and atomic permutations, while enabling end-to-end training and post-hoc Bayesian control without retraining. By integrating equivariant neural networks with conditional flow matching, EVFM unifies controllable generation and probabilistic inference, substantially enhancing symmetry awareness and control flexibility. Empirically, EVFM achieves state-of-the-art performance across both unconditional and diverse conditional molecular generation tasks—including property-guided and scaffold-constrained generation—demonstrating its effectiveness, generalizability, and scalability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Implement controlled generation via variational flow matching
• Enable equivariant molecular generation with symmetry constraints
• Bridge flow-based models and Bayesian inference for constraints

Innovation

• Controlled generation via Variational Flow Matching
• Equivariant VFM for invariant molecular generation
• Bayesian inference for post hoc model control