  While deep neural networks (NN) significantly advance image compressed
sensing (CS) by improving reconstruction quality, the necessity of training
current CS NNs from scratch constrains their effectiveness and hampers rapid
deployment. Although recent methods utilize pre-trained diffusion models for
image reconstruction, they struggle with slow inference and restricted
adaptability to CS. To tackle these challenges, this paper proposes Invertible
Diffusion Models (IDM), a novel efficient, end-to-end diffusion-based CS
method. IDM repurposes a large-scale diffusion sampling process as a
reconstruction model, and finetunes it end-to-end to recover original images
directly from CS measurements, moving beyond the traditional paradigm of
one-step noise estimation learning. To enable such memory-intensive end-to-end
finetuning, we propose a novel two-level invertible design to transform both
(1) the multi-step sampling process and (2) the noise estimation U-Net in each
step into invertible networks. As a result, most intermediate features are
cleared during training to reduce up to 93.8% GPU memory. In addition, we
develop a set of lightweight modules to inject measurements into noise
estimator to further facilitate reconstruction. Experiments demonstrate that
IDM outperforms existing state-of-the-art CS networks by up to 2.64dB in PSNR.
Compared to the recent diffusion model-based approach DDNM, our IDM achieves up
to 10.09dB PSNR gain and 14.54 times faster inference.
