Diversified Flow Matching with Translation Identifiability

TL;DR

This paper introduces diversified flow matching (DFM), an ODE-based framework for unpaired domain translation that guarantees translation identifiability, overcoming GAN limitations and providing useful transport trajectories.

Contribution

The work develops a novel ODE-based method for diversified distribution matching that ensures translation identifiability, with a new training loss, interpolant, and reformulation.

Findings

DFM guarantees translation identifiability in unpaired translation.

DFM outperforms GAN-based methods on synthetic and real datasets.

Transport trajectories are effectively obtained using DFM.

Abstract

Diversified distribution matching (DDM) finds a unified translation function mapping a diverse collection of conditional source distributions to their target counterparts. DDM was proposed to resolve content misalignment issues in unpaired domain translation, achieving translation identifiability. However, DDM has only been implemented using GANs due to its constraints on the translation function. GANs are often unstable to train and do not provide the transport trajectory information -- yet such trajectories are useful in applications such as single-cell evolution analysis and robot route planning. This work introduces diversified flow matching (DFM), an ODE-based framework for DDM. Adapting flow matching (FM) to enforce a unified translation function as in DDM is challenging, as FM learns the translation function's velocity rather than the translation function itself. A custom bilevel optimization-based training loss, a nonlinear interpolant, and a structural reformulation are proposed to address these challenges, offering a tangible implementation. To our knowledge, DFM is the first ODE-based approach guaranteeing translation identifiability. Experiments on synthetic and real-world datasets validate the proposed method.