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Finding Local Diffusion Schrodinger Bridge using Kolmogorov-Arnold Network
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Proposes Local Diffusion Schrödinger Bridge (LDSB), which optimizes the image and noise weights of a diffusion path with a tiny KAN (<0.1MB) while keeping the pretrained denoiser frozen, improving FID at low NFE for DDIM and flow matching.
Problem
Schrödinger bridge methods for image generation are computationally expensive and hard to train because they search globally optimal paths in high-dimensional space, while diffusion paths are typically predefined rather than optimized.
Approach
Restrict the Schrödinger bridge search to the diffusion path subspace parameterized by fA(t) and fB(t) (reparameterized as cumulative products of A(i), B(i)), optimize these weights iteratively with IPF-style losses using a small KAN, and keep the pretrained denoising network fixed.
Key results
- On CIFAR10 with DDIM at NFE=10, FID drops from 18.678 to 9.619 (48.50% reduction) with LDSB.
- On CelebA-HQ with flow matching at NFE=5, FID drops from 115.177 to 70.106 (39.13% reduction).
- The KAN used to optimize diffusion paths is 0.040 MB for 5 steps and 0.091 MB for 20 steps.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Optimize DDIM diffusion paths with LDSB | DDIM · CIFAR10, NFE 5 | FID: 44.394 -> 26.929 (↓39.34%) | Helped |
| Optimize DDIM diffusion paths with LDSB | DDIM · CIFAR10, NFE 10 | FID: 18.678 -> 9.619 (↓48.50%) | Helped |
| Optimize DDIM diffusion paths with LDSB | DDIM · CIFAR10, NFE 20 | FID: 11.080 -> 7.073 (↓36.16%) | Helped |
| Optimize DDIM diffusion paths with LDSB | DDIM · CelebA, NFE 5 | FID: 28.568 -> 18.757 (↓34.34%) | Helped |
| Optimize DDIM diffusion paths with LDSB | DDIM · CelebA, NFE 10 | FID: 18.042 -> 13.123 (↓27.26%) | Helped |
| Optimize DDIM diffusion paths with LDSB | DDIM · CelebA, NFE 20 | FID: 13.419 -> 9.987 (↓25.58%) | Helped |
| Optimize FM diffusion paths with LDSB | Flow Matching · CIFAR10, NFE 5 | FID: 35.493 -> 25.380 (↓28.49%) | Helped |
| Optimize FM diffusion paths with LDSB | Flow Matching · CIFAR10, NFE 10 | FID: 13.263 -> 10.989 (↓17.15%) | Helped |
| Optimize FM diffusion paths with LDSB | Flow Matching · CIFAR10, NFE 20 | FID: 7.309 -> 5.209 (↓28.73%) | Helped |
| Optimize FM diffusion paths with LDSB | Flow Matching · CelebA-HQ, NFE 5 | FID: 115.177 -> 70.106 (↓39.13%) | Helped |
| Optimize FM diffusion paths with LDSB | Flow Matching · CelebA-HQ, NFE 10 | FID: 62.041 -> 39.292 (↓36.67%) | Helped |
| Optimize FM diffusion paths with LDSB | Flow Matching · CelebA-HQ, NFE 20 | FID: 30.994 -> 26.108 (↓15.76%) | Helped |
Surprising findings
- LDSB with 10 DDIM steps on CIFAR10 (FID 9.619) beats the original 20-step DDIM (FID 11.080).
- An MLP in place of KAN for path optimization gives worse FID than the original path at NFE=5 on CIFAR10 (66.884 vs 44.394).
Limitations
- Gains are reported only on FID for three image datasets and two frameworks.
- Relies on the error of a fixed pretrained denoiser; the path is kept close to the original, limiting how far it can move.
Experimental setup
Datasets: CIFAR10 CelebA CelebA-HQ
Benchmarks: CIFAR10 CelebA CelebA-HQ
Metrics: FID
Baselines: DDIM Flow Matching DSB MLP-based path optimization
Builds on: Diffusion Schrödinger Bridge Simplified Diffusion Schrödinger Bridge DDIM flow matching Kolmogorov-Arnold Network
Closest papers by meaning
- Go With the Flow: Fast Diffusion for Gaussian Mixture Models (NeurIPS 2025 · similarity 0.89)
- Generalized Schrödinger Bridge Matching (ICLR 2024 · similarity 0.89)
- Adversarial Schrödinger Bridge Matching (NeurIPS 2024 · similarity 0.89)
- Variational Schrödinger Diffusion Models (ICML 2024 · similarity 0.88)
- Schrodinger Bridge Flow for Unpaired Data Translation (NeurIPS 2024 · similarity 0.88)
- Unpaired Image-to-Image Translation via Neural Schrödinger Bridge (ICLR 2024 · similarity 0.88)
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