用最优控制重写扩散模型，提升图像逆问题求解精度
Solving Inverse Problems via Diffusion Optimal Control
- 将逆问题转化为离散最优控制，避免依赖分数网络
- 在超分辨率、补全等任务上优于现有方法，重建更准
- 适用于各类线性非线性测量算子，通用性强
现有的基于扩散模型的逆问题求解方法将信号恢复视为从目标后验分布中采样，存在条件似然不可计算、严格依赖分数网络近似、初始状态预测质量差等问题。本文提出将生成过程重构为离散最优控制问题，设计了一种受迭代线性二次调节器（iLQR）启发的扩散最优控制器。该框架具有完全通用性，可处理任意可微的前向观测算子，包括超分辨率、图像补全、高斯模糊去卷积、非线性去模糊乃至高度非线性的神经分类器。进一步证明理想后验采样方程可作为本算法的特例。在多种神经逆问题求解器对比中，本方法建立了新的图像重建基准。
原文摘要 · Abstract (English)
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several critical drawbacks, including the intractability of the conditional likelihood function, strict dependence on the score network approximation, and poor $\mathbf{x}_0$ prediction quality. We demonstrate that these limitations can be sidestepped by reframing the generative process as a discrete optimal control episode. We derive a diffusion-based optimal controller inspired by the iterative Linear Quadratic Regulator (iLQR) algorithm. This framework is fully general and able to handle any differentiable forward measurement operator, including super-resolution, inpainting, Gaussian deblurring, nonlinear deblurring, and even highly nonlinear neural classifiers. Furthermore, we show that the idealized posterior sampling equation can be recovered as a special case of our algorithm. We then evaluate our method against a selection of neural inverse problem solvers, and establish a new baseline in image reconstruction with inverse problems.
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