Abstract
In image generation, Schrödinger 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 $f_A(t)$ and $f_B(t)$, as they follow the paradigm ($x_t = f_A(t)x_{Img} + f_B(t)\epsilon$). To address the limitations of SB-based methods, this paper proposes for the first time to find local Diffusion Schrödinger 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 \textbf{more than 15\%}, especially with a reduction of 48.50\% when NFE of DDIM is $5$ for the CelebA dataset. Code is available at this https URL.
Abstract (translated)
在图像生成领域，基于薛定谔桥（Schrödinger Bridge, SB）的方法理论上通过寻找两个分布之间的最低成本路径来提高效率和质量，相比扩散模型（diffusion models）有所改进。然而，在应用于复杂图像数据时，这些方法计算成本高昂且耗时长。原因是它们专注于在高维空间中拟合全局最优路径，并直接利用复杂的网络进行自监督训练生成下一步的图像，这通常会导致与全局最优解之间的差距。 另一方面，大多数扩散模型遵循范式 $(x_t = f_A(t)x_{\text{Img}} + f_B(t)\epsilon)$，它们也位于由权重 $f_A(t)$ 和 $f_B(t)$ 生成的路径子空间中。为了解决基于SB方法的局限性，本文首次提出在扩散路径子空间内寻找局部扩散薛定谔桥（Local Diffusion Schrödinger Bridge, LDSB），这加强了SB问题与扩散模型之间的联系。 具体来说，我们的方法使用Kolmogorov-Arnold网络（KAN）来优化扩散路径。该网络具有抵抗遗忘和连续输出的优点。实验表明，在使用相同的预训练去噪网络的情况下，LDSB显著提高了图像生成的质量和效率，并且用于优化的KAN模型大小仅为不到0.1MB。在CelebA数据集上，当DDIM的NFE为5时，FID度量减少了**超过15%**，特别是在这种情况下减少幅度达到了48.50%。 代码可以在以下网址获取：[此链接](https://this https URL) （请将“this https URL”替换为实际提供的链接）。
URL
https://arxiv.org/abs/2502.19754
