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Stochastic Interpolants with Data-Dependent Couplings
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Extends stochastic interpolants to data-dependent couplings between base and target densities, learning transport via square-loss regression, and applies it to ImageNet inpainting and super-resolution.
Problem
Generative models based on dynamical transport usually take an uninformative, data-agnostic base density (e.g. Gaussian) and independent coupling with the target, which yields complex transport paths; conditional settings do not exploit correlations between base and target samples.
Approach
Couple base and target through a conditional density rho_0(x0|x1) (e.g. x0 = m(x1) + sigma*zeta built from a corrupted observation), so the stochastic interpolant transports from a data-adapted base; the velocity and score are still learned by the same simple square-loss regression as in the independent setting.
Key results
- Dependent coupling achieves FID-50k 2.13 (train) / 2.05 (valid) on 64->256 ImageNet super-resolution, beating I2SB (2.70 valid) and other baselines.
- On ImageNet inpainting, dependent coupling reaches FID-50k 1.13 versus 1.35 for an uncoupled interpolant baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a data-dependent coupling instead of an independent Gaussian base coupling | Stochastic interpolant · ImageNet inpainting | FID-50k: 1.35 -> 1.13 | Helped |
| Use a data-dependent coupling instead of the strongest reported training baseline, Cascaded Diffusion | Dependent Coupling · ImageNet super-resolution, 64x64 to 256x256 (Train) | FID-50k: 4.88 -> 2.13 | Helped |
| Use a data-dependent coupling instead of the strongest reported validation baseline, I^2SB | Dependent Coupling · ImageNet super-resolution, 64x64 to 256x256 (Valid) | FID-50k: 2.70 -> 2.05 | Helped |
Limitations
- Experiments limited to image inpainting and super-resolution on ImageNet; no broader evaluation.
- Choice of data-dependent coupling is task-specific and must be designed by hand.
- Sampling via ODE yields a single output per base sample; SDE variants not experimentally explored.
Experimental setup
Datasets: ImageNet
Benchmarks: ImageNet 64x64 to 256x256 super-resolution (FID-50k) ImageNet inpainting (FID-50k)
Metrics: FID-50k
Baselines: Improved DDPM SR3 ADM Cascaded Diffusion I2SB Uncoupled Interpolant
Builds on: stochastic interpolants flow matching rectified flow I2SB
Closest papers by meaning
- Multimarginal Generative Modeling with Stochastic Interpolants (ICLR 2024 · similarity 0.91)
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