# Finding Local Diffusion Schr"odinger Bridge using Kolmogorov-Arnold Network

arXiv: https://arxiv.org/abs/2502.19754 · HTML: https://mlsanity.com/paper/2502.19754/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Residual Denoising Diffusion Models](https://mlsanity.com/paper/2308.13712/) (2023)
- [Light and Optimal Schr"odinger Bridge Matching](https://mlsanity.com/paper/2402.03207/) (2024)
- [Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis](https://mlsanity.com/paper/2312.03491/) (2023)
- [Schr"odinger bridge based deep conditional generative learning](https://mlsanity.com/paper/2409.17294/) (2024)

## Built on by (most cited first, 8 of 8)

- [IRBridge: Solving Image Restoration Bridge with Pre-trained Generative Diffusion Models](https://mlsanity.com/paper/2505.24406/) (2025)
- [Improving Memory Efficiency for Training KANs via Meta Learning](https://mlsanity.com/paper/2506.07549/) (2025)
- [Ambiguity-aware Truncated Flow Matching for Ambiguous Medical Image Segmentation](https://mlsanity.com/paper/2511.06857/) (2025)
- [Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.22409/) (2026)
- [Fully Kolmogorov-Arnold Deep Model in Medical Image Segmentation](https://mlsanity.com/paper/2602.03156/) (2026)
- [Timage: A Generative Text-in-Image Paradigm for Fine-Tuning Vision-Language Models](https://mlsanity.com/paper/2606.19944/) (2026)
- [GoodDiffusion: Proactive Copyright Protection for Diffusion Bridge Models via Learnable Sample-specific Signatures](https://mlsanity.com/paper/2606.29759/) (2026)
- [KANResDiff: Learning Local Residual Diffusion via Kolmogorov-Arnold Network for Ambiguous Medical Image Segmentation](https://mlsanity.com/paper/2608.11617/) (2026)

## Abstract (arXiv)

In image generation, Schr"odinger Bridge (SB)-based methods theoretically enhance the efficiency and quality compared to the diffusion models by finding the least costly path between two distributions. However, they are computationally expensive and time-consuming when applied to complex image data. The reason is that they focus on fitting globally optimal paths in high-dimensional spaces, directly generating images as next step on the path using complex networks through self-supervised training, which typically results in a gap with the global optimum. Meanwhile, most diffusion models are in the same path subspace generated by weights fA(t) and fB(t), as they follow the paradigm (xt = fA(t)xImg + fB(t)ε). To address the limitations of SB-based methods, this paper proposes for the first time to find local Diffusion Schr"odinger Bridges (LDSB) in the diffusion path subspace, which strengthens the connection between the SB problem and diffusion models. Specifically, our method optimizes the diffusion paths using Kolmogorov-Arnold Network (KAN), which has the advantage of resistance to forgetting and continuous output. The experiment shows that our LDSB significantly improves the quality and efficiency of image generation using the same pre-trained denoising network and the KAN for optimising is only less than 0.1MB. The FID metric is reduced by more than 15%, especially with a reduction of 48.50% when NFE of DDIM is 5 for the CelebA dataset. Code is available at https://github.com/PerceptionComputingLab/LDSB.