Controlled Generation with Equivariant Variational Flow Matching
This provides a principled framework for constraint-driven and symmetry-aware generation in domains like molecular design, though it builds incrementally on existing flow matching and Bayesian inference concepts.
The paper tackles controlled generation by developing a framework within Variational Flow Matching that enables constraint-driven generation through either end-to-end training or Bayesian inference without retraining, achieving state-of-the-art performance in both uncontrolled and controlled molecular generation.
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.