Chicago Y. Park

Chicago Y. Park, Weijie Gan, Zihao Zou et al.

Model-based deep learning (MBDL) is a powerful methodology for designing deep models to solve imaging inverse problems. MBDL networks can be seen as iterative algorithms that estimate the desired image using a physical measurement model and a learned image prior specified using a convolutional neural net (CNNs). The iterative nature of MBDL networks increases the test-time computational complexity, which limits their applicability in certain large-scale applications. Here we make two contributions to address this issue: First, we show how structured pruning can be adopted to reduce the number of parameters in MBDL networks. Second, we present three methods to fine-tune the pruned MBDL networks to mitigate potential performance loss. Each fine-tuning strategy has a unique benefit that depends on the presence of a pre-trained model and a high-quality ground truth. We show that our pruning and fine-tuning approach can accelerate image reconstruction using popular deep equilibrium learning (DEQ) and deep unfolding (DU) methods by 50% and 32%, respectively, with nearly no performance loss. This work thus offers a step forward for solving inverse problems by showing the potential of pruning to improve the scalability of MBDL. Code is available at https://github.com/wustl-cig/MBDL_Pruning .

Chicago Y. Park, Michael T. McCann, Cristina Garcia-Cardona et al.

We propose deep parameter interpolation (DPI), a general-purpose method for transforming an existing deep neural network architecture into one that accepts an additional scalar input. Recent deep generative models, including diffusion models and flow matching, employ a single neural network to learn a time- or noise level-dependent vector field. Designing a network architecture to accurately represent this vector field is challenging because the network must integrate information from two different sources: a high-dimensional vector (usually an image) and a scalar. Common approaches either encode the scalar as an additional image input or combine scalar and vector information in specific network components, which restricts architecture choices. Instead, we propose to maintain two learnable parameter sets within a single network and to introduce the scalar dependency by dynamically interpolating between the parameter sets based on the scalar value during training and sampling. DPI is a simple, architecture-agnostic method for adding scalar dependence to a neural network. We demonstrate that our method improves denoising performance and enhances sample quality for both diffusion and flow matching models, while achieving computational efficiency comparable to standard scalar conditioning techniques. Code is available at https://github.com/wustl-cig/parameter_interpolation.

Chicago Y. Park, Edward P. Chandler, Yuyang Hu et al.

Plug-and-play (PnP) methods are widely used for solving imaging inverse problems by incorporating a denoiser into optimization algorithms. Score-based diffusion models (SBDMs) have recently demonstrated strong generative performance through a denoiser trained across a wide range of noise levels. Despite their shared reliance on denoisers, it remains unclear how to systematically use SBDMs as priors within the PnP framework without relying on reverse diffusion sampling. In this paper, we establish a score-based interpretation of PnP that justifies using pretrained SBDMs directly within PnP algorithms. Building on this connection, we introduce a stochastic generative PnP (SGPnP) framework that injects noise to better leverage the expressive generative SBDM priors, thereby improving robustness in severely ill-posed inverse problems. We provide a new theory showing that this noise injection induces optimization on a Gaussian-smoothed objective and promotes escape from strict saddle points. Experiments on challenging inverse tasks, such as multi-coil MRI reconstruction and large-mask natural image inpainting, demonstrate consistent improvement over conventional PnP methods and achieve performance competitive with diffusion-based solvers.

Chicago Y. Park, Shirin Shoushtari, Hongyu An et al.

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce the Measurement Score-based diffusion Model (MSM), a novel framework that learns partial measurement scores using only noisy and subsampled measurements. MSM models the distribution of full measurements as an expectation over partial scores induced by randomized subsampling. To make the MSM representation computationally efficient, we also develop a stochastic sampling algorithm that generates full images by using a randomly selected subset of partial scores at each step. We additionally propose a new posterior sampling method for solving inverse problems that reconstructs images using these partial scores. We provide a theoretical analysis that bounds the Kullback-Leibler divergence between the distributions induced by full and stochastic sampling, establishing the accuracy of the proposed algorithm. We demonstrate the effectiveness of MSM on natural images and multi-coil MRI, showing that it can generate high-quality images and solve inverse problems -- all without access to clean training data. Code is available at https://github.com/wustl-cig/MSM.

Chicago Y. Park, Yuyang Hu, Michael T. McCann et al.

Plug-and-play (PnP) methods are extensively used for solving imaging inverse problems by integrating physical measurement models with pre-trained deep denoisers as priors. Score-based diffusion models (SBMs) have recently emerged as a powerful framework for image generation by training deep denoisers to represent the score of the image prior. While both PnP and SBMs use deep denoisers, the score-based nature of PnP is unexplored in the literature due to its distinct origins rooted in proximal optimization. This letter introduces a novel view of PnP as a score-based method, a perspective that enables the re-use of powerful SBMs within classical PnP algorithms without retraining. We present a set of mathematical relationships for adapting popular SBMs as priors within PnP. We show that this approach enables a direct comparison between PnP and SBM-based reconstruction methods using the same neural network as the prior. Code is available at https://github.com/wustl-cig/score_pnp.

Chicago Y. Park, Michael T. McCann, Cristina Garcia-Cardona et al.

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals -- particularly natural images -- and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.

Tingjun Liu, Chicago Y. Park, Yuyang Hu et al.

Diffusion-based inverse problem solvers (DIS) have recently shown outstanding performance in compressed-sensing parallel MRI reconstruction by combining diffusion priors with physical measurement models. However, they typically rely on pre-calibrated coil sensitivity maps (CSMs) and ground truth images, making them often impractical: CSMs are difficult to estimate accurately under heavy undersampling and ground-truth images are often unavailable. We propose Calibration-free Measurement Score-based diffusion Model (C-MSM), a new method that eliminates these dependencies by jointly performing automatic CSM estimation and self-supervised learning of measurement scores directly from k-space data. C-MSM reconstructs images by approximating the full posterior distribution through stochastic sampling over partial measurement posterior scores, while simultaneously estimating CSMs. Experiments on the multi-coil brain fastMRI dataset show that C-MSM achieves reconstruction performance close to DIS with clean diffusion priors -- even without access to clean training data and pre-calibrated CSMs.