Xinyu Peng

Xinyu Peng, Ziyang Zheng, Wenrui Dai et al.

Task-adapted compressed sensing magnetic resonance imaging (CS-MRI) is emerging to address the specific demands of downstream clinical tasks with significantly fewer k-space measurements than required by Nyquist sampling. However, existing task-adapted CS-MRI methods suffer from the uncertainty problem for medical diagnosis and cannot achieve adaptive sampling in end-to-end optimization with reconstruction or clinical tasks. To address these limitations, we propose the first task-adapted CS-MRI from the information-theoretic perspective to simultaneously achieve probabilistic inference for uncertainty prediction and adapt to arbitrary sampling ratios and versatile clinical applications. Specifically, we formalize the task-adapted CS-MRI optimization problem by maximizing the mutual information between undersampled k-space measurements and clinical tasks to enable probabilistic inference for addressing the uncertainty problem. We leverage amortized optimization and construct tractable variational bounds for mutual information to jointly optimize sampling, reconstruction, and task-inference models, which enables flexible sampling ratio control using a single end-to-end trained model. Furthermore, the proposed framework addresses two kinds of distinct clinical scenarios within a unified approach, i.e., i) joint task and reconstruction, where reconstruction serves as an auxiliary process to enhance task performance; and ii) task implementation with suppressed reconstruction, applicable for privacy protection. Extensive experiments on large-scale MRI datasets demonstrate that the proposed framework achieves highly competitive performance on standard metrics like Dice compared to deterministic counterpart but provides better distribution matching to the ground-truth posterior distribution as measured by the generalized energy distance (GED).

Xinyu Peng, Ziyang Zheng, Wenrui Dai et al.

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a Gaussian approximation with hand-crafted isotropic covariance for the intractable denoising posterior to approximate the conditional posterior mean. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation. To achieve posterior covariance optimization without retraining, we provide general plug-and-play solutions based on two approaches specifically designed for leveraging pre-trained models with and without reverse covariance. We further propose a scalable method for learning posterior covariance prediction based on representation with orthonormal basis. Experimental results demonstrate that the proposed methods significantly enhance reconstruction performance without requiring hyperparameter tuning.

Xinyu Peng, Ziyang Zheng, Yaoming Wang et al.

We propose Noise Conditional Variational Score Distillation (NCVSD), a novel method for distilling pretrained diffusion models into generative denoisers. We achieve this by revealing that the unconditional score function implicitly characterizes the score function of denoising posterior distributions. By integrating this insight into the Variational Score Distillation (VSD) framework, we enable scalable learning of generative denoisers capable of approximating samples from the denoising posterior distribution across a wide range of noise levels. The proposed generative denoisers exhibit desirable properties that allow fast generation while preserve the benefit of iterative refinement: (1) fast one-step generation through sampling from pure Gaussian noise at high noise levels; (2) improved sample quality by scaling the test-time compute with multi-step sampling; and (3) zero-shot probabilistic inference for flexible and controllable sampling. We evaluate NCVSD through extensive experiments, including class-conditional image generation and inverse problem solving. By scaling the test-time compute, our method outperforms teacher diffusion models and is on par with consistency models of larger sizes. Additionally, with significantly fewer NFEs than diffusion-based methods, we achieve record-breaking LPIPS on inverse problems.