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Adversarial Schrödinger Bridge Matching
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Proposes discrete-time Iterative Markovian Fitting (D-IMF) for the Schrödinger Bridge, implemented as ASBM with DD-GAN-style adversarial transition learning, reaching IMF-level unpaired translation quality in 4 steps instead of ~100.
Problem
Solving the Schrödinger Bridge via Iterative Markovian Fitting requires learning continuous-time SDEs whose numerical solvers need many steps, making inference slow.
Approach
Replace continuous-time Markovian projection with discrete-time Markovian projection that only learns a few transition probabilities between intermediate times, each learned with an adversarial (DD-GAN) time-conditioned generator; the procedure provably converges to the SB and admits closed-form Gaussian updates.
Key results
- ASBM with 4 NFE achieves FID 16.08 (epsilon=1) on CelebA male-to-female vs DSBM FID 37.8 at NFE 100.
- ASBM with epsilon=10 reaches FID 17.44 at 4 NFE vs DSBM FID 89.19 at 100 NFE.
- On Gaussian setups D-IMF shows empirically exponential convergence to the static SB solution, with convergence speed saturating quickly in N (N=5 already fast).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace DSBM with ASBM | CelebA male→female translation, ε=1 · CelebA male→female, ε=1 | FID: 37.8 -> 16.08 | Helped |
| replace DSBM with ASBM | CelebA male→female translation, ε=10 · CelebA male→female, ε=10 | FID: 89.19 -> 17.44 | Helped |
| replace DSBM with ASBM | CelebA male→female translation, ε=1 · CelebA male→female, ε=1 | NFE: 100 -> 4 | Helped |
| replace DSBM with ASBM | CelebA male→female translation, ε=10 · CelebA male→female, ε=10 | NFE: 100 -> 4 | Helped |
| increase ε from 1 to 10 | Gaussian-to-Gaussian D-IMF convergence · Gaussian-to-Gaussian Schrödinger Bridge | D-IMF iterations to converge: ten times more D-IMF iterations | Hurt |
Surprising findings
- Convergence speed of D-IMF depends strongly on epsilon: going from epsilon=1 to epsilon=10 needs about ten times more iterations.
Limitations
- Adversarial training can be unstable; relies on DD-GAN backbone practices.
- Theoretical convergence rate is not proven; only empirical exponential rate on Gaussians.
- Markovian projection in discrete time differs from continuous-time projection, so the method is not exactly IMF.
Experimental setup
Datasets: CelebA Gaussian synthetic distributions (D=16)
Benchmarks: CelebA male-to-female translation (128x128)
Metrics: FID NFE KL divergence to static SB solution
Baselines: DSBM IMF
Builds on: Iterative Markovian Fitting Bridge Matching Denoising Diffusion GAN DSBM Rectified Flow
Closest papers by meaning
- Schrodinger Bridge Flow for Unpaired Data Translation (NeurIPS 2024 · similarity 0.92)
- Unpaired Image-to-Image Translation via Neural Schrödinger Bridge (ICLR 2024 · similarity 0.90)
- Generalized Schrödinger Bridge Matching (ICLR 2024 · similarity 0.89)
- Exponential Convergence Guarantees for Iterative Markovian Fitting (NeurIPS 2025 · similarity 0.89)
- Finding Local Diffusion Schrodinger Bridge using Kolmogorov-Arnold Network (CVPR 2025 · similarity 0.89)
- Discrete Diffusion Schrödinger Bridge Matching for Graph Transformation (ICLR 2025 · similarity 0.88)
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