用离散扩散模型解决逆问题，内存更低且效果接近连续方法
G2D2: Gradient-Guided Discrete Diffusion for Inverse Problem Solving
- 用类别分布和连续松弛构造变分后验，突破离散模型限制
- 星形噪声过程避免吸收态问题，线性逆问题求解性能接近连续扩散
- 适合图像、动作生成等离散压缩表示场景，显存占用更少
近期研究已有效利用基于连续变量的扩散模型作为先验求解逆问题。值得注意的是，基于离散潜在码的离散扩散模型在图像、动作生成等适合离散压缩表示的模态中表现优异。然而，其离散性和不可微特性限制了在连续空间设定下的逆问题应用。本文提出一种新方法，利用基于离散扩散的生成模型作为先验，解决线性逆问题。我们通过类别分布与连续松弛技术构建变分后验，逼近真实后验分布。此外，采用星形噪声过程缓解传统离散扩散模型中吸收态的缺陷，实验表明该方法性能可媲美连续扩散技术，且GPU内存消耗更低。代码已开源：https://github.com/sony/g2d2。
原文摘要 · Abstract (English)
Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly in modalities suited for discrete compressed representations, such as image and motion generation. However, their discrete and non-differentiable nature has limited their application to inverse problems formulated in continuous spaces. This paper presents a novel method for addressing linear inverse problems by leveraging generative models based on discrete diffusion as priors. We overcome these limitations by approximating the true posterior distribution with a variational distribution constructed from categorical distributions and continuous relaxation techniques. Furthermore, we employ a star-shaped noise process to mitigate the drawbacks of traditional discrete diffusion models with absorbing states, demonstrating that our method performs comparably to continuous diffusion techniques with a lower GPU memory consumption. Our code is available at https://github.com/sony/g2d2.
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