Recently it has been shown that using diffusion models for inverse problems
can lead to remarkable results. However, these approaches require a closed-form
expression of the degradation model and can not support complex degradations.
To overcome this limitation, we propose a method (INDigo) that combines
invertible neural networks (INN) and diffusion models for general inverse
problems. Specifically, we train the forward process of INN to simulate an
arbitrary degradation process and use the inverse as a reconstruction process.
During the diffusion sampling process, we impose an additional data-consistency
step that minimizes the distance between the intermediate result and the
INN-optimized result at every iteration, where the INN-optimized image is
composed of the coarse information given by the observed degraded image and the
details generated by the diffusion process. With the help of INN, our algorithm
effectively estimates the details lost in the degradation process and is no
longer limited by the requirement of knowing the closed-form expression of the
degradation model. Experiments demonstrate that our algorithm obtains
competitive results compared with recently leading methods both quantitatively
and visually. Moreover, our algorithm performs well on more complex degradation
models and real-world low-quality images.

该研究提出了一种结合可逆神经网络和扩散模型的方法（INDigo）来解决逆问题，同时在扩散过程中添加数据一致性步骤来优化重建图像，实验表明该方法可以在更多复杂的退化模型和低质量图像上表现良好。

INDigo：基于 INN 引导的概率扩散算法解逆问题

INDigo: An INN-Guided Probabilistic Diffusion Algorithm for Inverse  Problems

We introduce a model-based image reconstruction framework with a convolution
neural network (CNN) based regularization prior. The proposed formulation
provides a systematic approach for deriving deep architectures for inverse
problems with the arbitrary structure. Since the forward model is explicitly
accounted for, a smaller network with fewer parameters is sufficient to capture
the image information compared to black-box deep learning approaches, thus
reducing the demand for training data and training time. Since we rely on
end-to-end training, the CNN weights are customized to the forward model, thus
offering improved performance over approaches that rely on pre-trained
denoisers. The main difference of the framework from existing end-to-end
training strategies is the sharing of the network weights across iterations and
channels. Our experiments show that the decoupling of the number of iterations
from the network complexity offered by this approach provides benefits
including lower demand for training data, reduced risk of overfitting, and
implementations with significantly reduced memory footprint. We propose to
enforce data-consistency by using numerical optimization blocks such as
conjugate gradients algorithm within the network; this approach offers faster
convergence per iteration, compared to methods that rely on proximal gradients
steps to enforce data consistency. Our experiments show that the faster
convergence translates to improved performance, especially when the available
GPU memory restricts the number of iterations.

该研究提出了一种基于卷积神经网络的模型重建框架，实现了解决逆问题的途径。该框架克服了深度学习方法中过多参数所占用的训练数据和时间上的需求问题，并在重构图像方面取得了显著成果。