Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains under-explored, which hinders understanding the controllability of the sampling process. In this work, we first observe an interesting phenomenon: the relationship between the change of generation outputs and the scale of initial noise perturbation is highly linear through the diffusion ODE sampling. Then we provide both theoretical and empirical study to justify this linearity property of this input-output (noise-generation data) relationship. Inspired by these new insights, we propose a novel Controllable and Constrained Sampling method (CCS) together with a new controller algorithm for diffusion models to sample with desired statistical properties while preserving good sample quality. We perform extensive experiments to compare our proposed sampling approach with other methods on both sampling controllability and sampled data quality. Results show that our CCS method achieves more precisely controlled sampling while maintaining superior sample quality and diversity.

During and after a course of therapy, imaging is routinely used to monitor the disease progression and assess the treatment responses. Despite of its significance, reliably capturing and predicting the spatial-temporal anatomic changes from a sequence of patient-specific image series presents a considerable challenge. Thus, the development of a computational framework becomes highly desirable for a multitude of practical applications. In this context, we propose a strategy of Spatial-Temporal Neural Representation learning with Prior embedding (ST-NeRP) for patient-specific imaging study. Our strategy involves leveraging an Implicit Neural Representation (INR) network to encode the image at the reference time point into a prior embedding. Subsequently, a spatial-temporally continuous deformation function is learned through another INR network. This network is trained using the whole patient-specific image sequence, enabling the prediction of deformation fields at various target time points. The efficacy of the ST-NeRP model is demonstrated through its application to diverse sequential image series, including 4D CT and longitudinal CT datasets within thoracic and abdominal imaging. The proposed ST-NeRP model exhibits substantial potential in enabling the monitoring of anatomical changes within a patient throughout the therapeutic journey.

Diffusion models have achieved excellent success in solving inverse problems due to their ability to learn strong image priors, but existing approaches require a large training dataset of images that should come from the same distribution as the test dataset. When the training and test distributions are mismatched, artifacts and hallucinations can occur in reconstructed images due to the incorrect priors. In this work, we systematically study out of distribution (OOD) problems where a known training distribution is first provided. We first study the setting where only a single measurement obtained from the unknown test distribution is available. Next we study the setting where a very small sample of data belonging to the test distribution is available, and our goal is still to reconstruct an image from a measurement that came from the test distribution. In both settings, we use a patch-based diffusion prior that learns the image distribution solely from patches. Furthermore, in the first setting, we include a self-supervised loss that helps the network output maintain consistency with the measurement. Extensive experiments show that in both settings, the patch-based method can obtain high quality image reconstructions that can outperform whole-image models and can compete with methods that have access to large in-distribution training datasets. Furthermore, we show how whole-image models are prone to memorization and overfitting, leading to artifacts in the reconstructions, while a patch-based model can resolve these issues. In image processing, inverse problems are of paramount importance and consist of reconstructing a latent image x from a measurement y = A(x) + ε. Here, A represents a forward operator and ε represents random unknown noise. By Bayes' rule, log p(x|y) is proportional to log p(x) + log p(y|x), so obtaining a good prior p(x) is crucial for recovering x when y contains far less information than x.

Diffusion models can learn strong image priors from underlying data distribution and use them to solve inverse problems, but the training process is computationally expensive and requires lots of data. Such bottlenecks prevent most existing works from being feasible for high-dimensional and high-resolution data such as 3D images. This paper proposes a method to learn an efficient data prior for the entire image by training diffusion models only on patches of images. Specifically, we propose a patch-based position-aware diffusion inverse solver, called PaDIS, where we obtain the score function of the whole image through scores of patches and their positional encoding and utilize this as the prior for solving inverse problems. First of all, we show that this diffusion model achieves an improved memory efficiency and data efficiency while still maintaining the capability to generate entire images via positional encoding. Additionally, the proposed PaDIS model is highly flexible and can be plugged in with different diffusion inverse solvers (DIS). We demonstrate that the proposed PaDIS approach enables solving various inverse problems in both natural and medical image domains, including CT reconstruction, deblurring, and superresolution, given only patch-based priors. Notably, PaDIS outperforms previous DIS methods trained on entire image priors in the case of limited training data, demonstrating the data efficiency of our proposed approach by learning patch-based prior.

Vision-language pre-training (VLP) has arised as an efficient scheme for multimodal representation learning, but it requires large-scale multimodal data for pre-training, making it an obstacle especially for medical applications. To overcome the data limitation, federated learning (FL) can be a promising strategy to scale up the dataset for medical VLP while protecting data privacy. However, client data are often heterogeneous in real-world scenarios, and we observe that local training on heterogeneous client data would distort the multimodal representation learning and lead to biased cross-modal alignment. To address this challenge, we propose a Federated Align as IDeal (FedAID) framework for federated VLP with robustness to data heterogeneity, to bind local clients with an ideal crossmodal alignment. Specifically, to reduce distortions on global-aggregated features while learning diverse semantics from client datasets during local training, we propose to bind the cross-model aligned representation space learned by local models with an unbiased one via guidance-based regularization. Moreover, we employ a distribution-based min-max optimization to learn the unbiased cross-modal alignment at each communication turn of federated pre-training. The experiments on real-world datasets demonstrate our method successfully promotes efficient federated multimodal learning for medical VLP with data heterogeneity.

The collaborative nature of federated learning (FL) poses a major threat in the form of manipulation of local training data and local updates, known as the Byzantine poisoning attack. To address this issue, many Byzantine-robust aggregation rules (AGRs) have been proposed to filter out or moderate suspicious local updates uploaded by Byzantine participants. This paper introduces a novel approach called AGRAMPLIFIER, aiming to simultaneously improve the robustness, fidelity, and efficiency of the existing AGRs. The core idea of AGRAMPLIFIER is to amplify the "morality" of local updates by identifying the most repressive features of each gradient update, which provides a clearer distinction between malicious and benign updates, consequently improving the detection effect. To achieve this objective, two approaches, namely AGRMP and AGRXAI, are proposed. AGRMP organizes local updates into patches and extracts the largest value from each patch, while AGRXAI leverages explainable AI methods to extract the gradient of the most activated features. By equipping AGRAMPLIFIER with the existing Byzantine-robust mechanisms, we successfully enhance the model's robustness, maintaining its fidelity and improving overall efficiency. AGRAMPLIFIER is universally compatible with the existing Byzantine-robust mechanisms. The paper demonstrates its effectiveness by integrating it with all mainstream AGR mechanisms. Extensive evaluations conducted on seven datasets from diverse domains against seven representative poisoning attacks consistently show enhancements in robustness, fidelity, and efficiency, with average gains of 40.08%, 39.18%, and 10.68%, respectively.

Recently, diffusion models have emerged as powerful deep generative models, showcasing cutting-edge performance across various applications such as image generation, solving inverse problems, and text-to-image synthesis. These models generate new data (e.g., images) by transforming random noise inputs through a reverse diffusion process. In this work, we uncover a distinct and prevalent phenomenon within diffusion models in contrast to most other generative models, which we refer to as ``consistent model reproducibility''. To elaborate, our extensive experiments have consistently shown that when starting with the same initial noise input and sampling with a deterministic solver, diffusion models tend to produce nearly identical output content. This consistency holds true regardless of the choices of model architectures and training procedures. Additionally, our research has unveiled that this exceptional model reproducibility manifests in two distinct training regimes: (i) ``memorization regime,'' characterized by a significantly overparameterized model which attains reproducibility mainly by memorizing the training data; (ii) ``generalization regime,'' in which the model is trained on an extensive dataset, and its reproducibility emerges with the model's generalization capabilities. Our analysis provides theoretical justification for the model reproducibility in ``memorization regime''. Moreover, our research reveals that this valuable property generalizes to many variants of diffusion models, including conditional diffusion models, diffusion models for solving inverse problems, and fine-tuned diffusion models. A deeper understanding of this phenomenon has the potential to yield more interpretable and controllable data generative processes based on diffusion models.

Phase retrieval (PR) is a crucial problem in many imaging applications. This study focuses on resolving the holographic phase retrieval problem in situations where the measurements are affected by a combination of Poisson and Gaussian noise, which commonly occurs in optical imaging systems. To address this problem, we propose a new algorithm called "AWFS" that uses the accelerated Wirtinger flow (AWF) with a score function as generative prior. Specifically, we formulate the PR problem as an optimization problem that incorporates both data fidelity and regularization terms. We calculate the gradient of the log-likelihood function for PR and determine its corresponding Lipschitz constant. Additionally, we introduce a generative prior in our regularization framework by using score matching to capture information about the gradient of image prior distributions. We provide theoretical analysis that establishes a critical-point convergence guarantee for the proposed algorithm. The results of our simulation experiments on three different datasets show the following: 1) By using the PG likelihood model, the proposed algorithm improves reconstruction compared to algorithms based solely on Gaussian or Poisson likelihood. 2) The proposed score-based image prior method, performs better than the method based on denoising diffusion probabilistic model (DDPM), as well as plug-and-play alternating direction method of multipliers (PnP-ADMM) and regularization by denoising (RED).

The collection and curation of large-scale medical datasets from multiple institutions is essential for training accurate deep learning models, but privacy concerns often hinder data sharing. Federated learning (FL) is a promising solution that enables privacy-preserving collaborative learning among different institutions, but it generally suffers from performance deterioration due to heterogeneous data distributions and a lack of quality labeled data. In this paper, we present a robust and label-efficient self-supervised FL framework for medical image analysis. Our method introduces a novel Transformer-based self-supervised pre-training paradigm that pre-trains models directly on decentralized target task datasets using masked image modeling, to facilitate more robust representation learning on heterogeneous data and effective knowledge transfer to downstream models. Extensive empirical results on simulated and real-world medical imaging non-IID federated datasets show that masked image modeling with Transformers significantly improves the robustness of models against various degrees of data heterogeneity. Notably, under severe data heterogeneity, our method, without relying on any additional pre-training data, achieves an improvement of 5.06%, 1.53% and 4.58% in test accuracy on retinal, dermatology and chest X-ray classification compared to the supervised baseline with ImageNet pre-training. In addition, we show that our federated self-supervised pre-training methods yield models that generalize better to out-of-distribution data and perform more effectively when fine-tuning with limited labeled data, compared to existing FL algorithms. The code is available at https://github.com/rui-yan/SSL-FL.

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes. Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are commonly used imaging tools for medical diagnosis. Reconstructing CT and MRI images from raw measurements (sinograms for CT and k-spaces for MRI) are well-known inverse problems. Specifically, measurements in CT are given by X-ray projections of an object from various directions, and measurements in MRI are obtained by inspecting the Fourier spectrum of an object with magnetic fields.