用动态投影加速扩散模型，10-50倍提升线性逆问题求解速度
Linearly Constrained Diffusion Implicit Models
- 根据前向扩散过程理论分布，自适应调整投影次数与大小
- 噪声无时仅需少量投影即精确满足测量约束，现有方法失败时仍有效
- 适用于超分、去噪、修复等任务，支持快速交互式推理
我们提出线性约束扩散隐式模型（CDIM），一种快速且精准求解含噪线性逆问题的新方法。传统基于扩散的逆问题求解依赖大量投影步骤以保证测量一致性，同时还需无条件去噪。CDIM通过动态调节投影步数与规模，使残差测量能量与前向扩散过程下的理论分布对齐，实现10-50倍投影步骤减少。该自适应对齐在保持测量一致性的前提下显著加速约束推断。对于无噪线性逆问题，即使现有方法失效，CDIM也能以极少投影步骤精确满足测量约束。我们在超分辨率、去噪、修复、去模糊及3D点云重投影等多种应用中验证了CDIM的有效性。代码与交互式演示可在项目主页获取。
原文摘要 · Abstract (English)
We introduce Linearly Constrained Diffusion Implicit Models (CDIM), a fast and accurate approach to solving noisy linear inverse problems using diffusion models. Traditional diffusion-based inverse methods rely on numerous projection steps to enforce measurement consistency in addition to unconditional denoising steps. CDIM achieves a 10-50x reduction in projection steps by dynamically adjusting the number and size of projection steps to align a residual measurement energy with its theoretical distribution under the forward diffusion process. This adaptive alignment preserves measurement consistency while substantially accelerating constrained inference. For noise-free linear inverse problems, CDIM exactly satisfies the measurement constraints with few projection steps, even when existing methods fail. We demonstrate CDIM's effectiveness across a range of applications, including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reprojection. Code and an interactive demo can be found on our project website.
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