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Feedback Schrödinger Bridge Matching
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Proposes Feedback Schrödinger Bridge Matching (FSBM), a semi-supervised matching framework that uses a small set of pre-aligned pairs as state feedback to guide transport of non-coupled samples.
Problem
Diffusion/Schrödinger bridge matching methods either need fully unsupervised training (costly, slow) or fully supervised optimal pairings (infeasible in many applications); partially aligned datasets are not exploited effectively.
Approach
Formulate a static semi-supervised entropic OT with a distance-preserving guidance term defined by nearest key-point pairs, recast it as a dynamic objective with a state-feedback term, and train via alternating intermediate-path optimization and Bregman-divergence bridge matching.
Key results
- On FFHQ translation, FSBM achieves lower FID than DSBM and LOSBM across 4 translation tasks while using about 180 MB extra VRAM over DSBM.
- In crowd navigation, FSBM with fewer than 4% aligned pairs trains significantly faster than GSBM and generalizes better under perturbed initial conditions.
- In 100-dimensional opinion dynamics, FSBM with about 2% KP samples reaches slightly closer W2/KL to target than GSBM at half the training time.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FSBM instead of GSBM | Crowd Navigation: S-tunnel and V-neck · Crowd Navigation, perturbed and uniform initial conditions | W₂ distance | Helped |
| Use FSBM instead of GSBM | Crowd Navigation: S-tunnel and V-neck · Crowd Navigation | training time | Helped |
| Use FSBM instead of GSBM | High-dimensional Opinion Dynamics · Opinion Dynamics, X∈ℝ¹⁰⁰ | W₂ distance | Helped |
| Use FSBM instead of GSBM | High-dimensional Opinion Dynamics · Opinion Dynamics, X∈ℝ¹⁰⁰ | training time | Helped |
| Use FSBM instead of DSBM and LOSBM | Image Translation · Gender and age translation | FID | Helped |
| Use FSBM instead of DSBM | Image Translation · Gender and age translation | LPIPS | No clear effect |
| Use FSBM instead of DSBM | Image Translation · Age translation | VRAM usage: 180 MB | Hurt |
| Train FSBM for the same number of epochs as DSBM | Image Translation · Age translation | training duration | No clear effect |
Limitations
- Performance depends heavily on the availability and quality of key-point pairs.
- Sampling from the static SB solution does not guarantee coverage of all modes, so sparse KP sets can give wrong guidance.
- Guidance uses only the single nearest key-point rather than k-nearest neighbours.
Experimental setup
Datasets: FFHQ crowd navigation simulated data opinion dynamics simulated data
Benchmarks: FFHQ gender translation FFHQ age translation crowd navigation opinion dynamics
Metrics: W2 distance KL divergence FID LPIPS training wall-clock time
Baselines: GSBM DSBM LOSBM DeepGSB I^2SB
Builds on: Schrödinger Bridge Matching Diffusion Schrödinger Bridge Matching Bridge Matching Iterative Proportional Fitting
Closest papers by meaning
- Light and Optimal Schrödinger Bridge Matching (ICML 2024 · similarity 0.93)
- Generalized Schrödinger Bridge Matching (ICLR 2024 · similarity 0.92)
- Momentum Multi-Marginal Schrödinger Bridge Matching (NeurIPS 2025 · similarity 0.91)
- Discrete Diffusion Schrödinger Bridge Matching for Graph Transformation (ICLR 2025 · similarity 0.90)
- Schrödinger Bridge Matching for Tree-Structured Costs and Entropic Wasserstein Barycentres (NeurIPS 2025 · similarity 0.89)
- Go With the Flow: Fast Diffusion for Gaussian Mixture Models (NeurIPS 2025 · similarity 0.89)
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