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Diversified Flow Matching with Translation Identifiability
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Proposes diversified flow matching (DFM), an ODE-based flow matching framework that enforces the DDM unified-translation criterion via private learnable nonlinear interpolants and a bilevel loss, simplified to a two-stage training scheme, giving translation identifiability.
Problem
Unpaired domain translation suffers from content misalignment because translation functions are not identifiable; DDM guarantees identifiability but has only been implemented with GANs, which are unstable and do not give transport trajectories.
Approach
Replace linear interpolants with private, learnable nonlinear interpolants per conditional pair, and use a bilevel loss (later reduced to a two-stage scheme exploiting non-overlapping supports) so that a single unified velocity field satisfies DDM and thus recovers the identifiable translation function.
Key results
- On Face to Bitmoji, DFM achieves FID 22.20 and DreamSim 0.59, the best FID among methods (DDM-GAN 26.20, FM-cond 22.65, FM 43.23).
- On synthetic 2D Gaussians, DFM reduces EMD to 0.31 and translation error to 2.42 versus about 9.6 and 9.9 for FM-cond baselines.
- On swarm navigation, DFM attains surface adherence 0.32 versus 0.43 to 1.09 for baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use private learnable nonlinear, non-intersecting interpolants with DFM instead of auxiliary-conditioned FM-OT | FM-cond-OT · 2D Gaussians | EMD: 9.56 $\pm$ 0.41 -> 0.31 $\pm$ 0.06 | Helped |
| Use private learnable nonlinear, non-intersecting interpolants with DFM instead of auxiliary-conditioned FM-OT | FM-cond-OT · 3D Gaussians | TE: 9.994 $\pm$ 0.428 -> 3.196 $\pm$ 0.034 | Helped |
| Use DFM instead of FM-cond | FM-cond · Face to Bitmoji | FID: 22.65 -> 22.20 | Helped |
| Use DFM instead of FM-cond | FM-cond · Face to Bitmoji | DreamSim: 0.60 (0.06) -> 0.59 (0.05) | Helped |
| Use DFM instead of MFM-cond-OT | MFM-cond-OT · Swarm navigation | SA: 0.43 $\pm$ 0.055 -> 0.32 $\pm$ 0.080 | Helped |
| Add auxiliary gender conditioning to plain FM | FM · Face to Bitmoji | FID: 43.23 -> 22.65 | Helped |
Surprising findings
- Naive FM with linear interpolants and summed per-pair losses fails to satisfy DDM, producing 'reflection' of trajectories toward the cluster mean.
- DDM-GAN training showed erratic FID convergence issues on the face translation task.
Limitations
- Restricted to one-to-one translations; one-to-many not handled.
- Efficient computing scheme relies on non-overlapping supports of conditional distributions.
- Image experiments use interleaved training and a modified algorithm, deviating from the theoretical two-stage procedure.
Experimental setup
Datasets: CelebA-HQ Bitmoji faces Mt. Rainier LiDAR point cloud synthetic 2D/3D Gaussian blobs
Benchmarks: Face to Bitmoji translation synthetic 2D/3D Gaussian blobs Mt. Rainier swarm navigation
Metrics: FID DreamSim EMD translation error surface adherence train time inference time
Baselines: FM FM-OT FM-cond FM-cond-OT MFM-OT MFM-cond-OT CycleGAN DDM-GAN SDEdit EGSDE
Builds on: flow matching diversified distribution matching DDM-GAN CycleGAN metric flow matching
Closest papers by meaning
- Optimal Flow Matching: Learning Straight Trajectories in Just One Step (NeurIPS 2024 · similarity 0.86)
- Switched Flow Matching: Eliminating Singularities via Switching ODEs (ICML 2024 · similarity 0.85)
- Towards Identifiable Unsupervised Domain Translation: A Diversified Distribution Matching Approach (ICLR 2024 · similarity 0.85)
- Improving Flow Matching by Aligning Flow Divergence (ICML 2025 · similarity 0.84)
- Value Gradient Guidance for Flow Matching Alignment (NeurIPS 2025 · similarity 0.84)
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