# Controlled Generation with Equivariant Variational Flow Matching

Source: [Controlled Generation with Equivariant Variational Flow Matching](<https://www.sota2.com/research/paper/68fa7be41e209131cea8b177>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:57:22.596Z

Authors: Floor Eijkelboom, Heiko Zimmermann, Sharvaree Vadgama, Erik J Bekkers, Max Welling, Christian A. Naesseth, Jan-Willem van de Meent

Published: 2025-06-23T06:42:48.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Property Optimization on MOSES ~1.5M molecules (test)](<https://www.sota2.com/research/sota/property-optimization-on-moses-1-5m-molecules-test.md>): Property optimization; MOSES ~1.5M molecules (test); C.V.U.N. Score: 72.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2506.18340>)

[PDF](<https://arxiv.org/pdf/2506.18340.pdf>)