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We introduce the Joint Video-Image Diffusion model (JVID), a novel approach to generating high-quality and temporally coherent videos. We achieve this by integrating two diffusion models: a Latent Image Diffusion Model (LIDM) trained on images and a Latent Video Diffusion Model (LVDM) trained on video data. Our method combines these models in the reverse diffusion process, where the LIDM enhances image quality and the LVDM ensures temporal consistency. This unique combination allows us to effectively handle the complex spatio-temporal dynamics in video generation. Our results demonstrate quantitative and qualitative improvements in producing realistic and coherent videos.

Physics-Informed Neural Networks (PINNs) are fast becoming an important tool to solve differential equations rapidly and accurately, and to identify the systems parameters that best agree with a given set of measurements. PINNs have been used for cardiac electrophysiology (EP), but only in simple 1D and 2D geometries and for sinus rhythm or single rotor dynamics. Here, we demonstrate how PINNs can be used to accurately reconstruct the propagation of cardiac action potential in more complex geometries and dynamical regimes. These include 3D spherical geometries and spiral break-up conditions that model cardiac fibrillation, with a mean RMSE $< 5.1\times 10^{-2}$ overall. We also demonstrate that PINNs can be used to reliably parameterise cardiac EP models with some biological detail. We estimate the diffusion coefficient and parameters related to ion channel conductances in the Fenton-Karma model in a 2D setup, achieving a mean relative error of $-0.09\pm 0.33$. Our results are an important step towards the deployment of PINNs to realistic cardiac geometries and arrhythmic conditions., Comment: Accepted for publication in the 15th Statistical Atlases and Computational Modeling of the Heart (STACOM) workshop 2024; 12 pages

While deep learning techniques have proven successful in image-related tasks, the exponentially increased data storage and computation costs become a significant challenge. Dataset distillation addresses these challenges by synthesizing only a few images for each class that encapsulate all essential information. Most current methods focus on matching. The problems lie in the synthetic images not being human-readable and the dataset performance being insufficient for downstream learning tasks. Moreover, the distillation time can quickly get out of bounds when the number of synthetic images per class increases even slightly. To address this, we train a class conditional latent diffusion model capable of generating realistic synthetic images with labels. The sampling time can be reduced to several tens of images per seconds. We demonstrate that models can be effectively trained using only a small set of synthetic images and evaluated on a large real test set. Our approach achieved rank \(1\) in The First Dataset Distillation Challenge at ECCV 2024 on the CIFAR100 and TinyImageNet datasets., Comment: 13 pages, 7 figures

Diagnosing medical conditions from histopathology data requires a thorough analysis across the various resolutions of Whole Slide Images (WSI). However, existing generative methods fail to consistently represent the hierarchical structure of WSIs due to a focus on high-fidelity patches. To tackle this, we propose Ultra-Resolution Cascaded Diffusion Models (URCDMs) which are capable of synthesising entire histopathology images at high resolutions whilst authentically capturing the details of both the underlying anatomy and pathology at all magnification levels. We evaluate our method on three separate datasets, consisting of brain, breast and kidney tissue, and surpass existing state-of-the-art multi-resolution models. Furthermore, an expert evaluation study was conducted, demonstrating that URCDMs consistently generate outputs across various resolutions that trained evaluators cannot distinguish from real images. All code and additional examples can be found on GitHub., Comment: arXiv admin note: text overlap with arXiv:2312.01152

Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for example when reconstructing clean images from poor signals. Diffusion models have shown promise as potent generative tools for solving inverse problems due to their superior reconstruction quality and their compatibility with iterative solvers. However, most existing approaches are limited to linear inverse problems represented as Stochastic Differential Equations (SDEs). This simplification falls short of addressing the challenging nature of real-world problems, leading to amplified cumulative errors and biases. We provide an explanation for this gap through the lens of measure-preserving dynamics of Random Dynamical Systems (RDS) with which we analyse Temporal Distribution Discrepancy and thus introduce a theoretical framework based on RDS for SDE diffusion models. We uncover several strategies that inherently enhance the stability and generalizability of diffusion models for inverse problems and introduce a novel score-based diffusion framework, the \textbf{D}ynamics-aware S\textbf{D}E \textbf{D}iffusion \textbf{G}enerative \textbf{M}odel (D$^3$GM). The \textit{Measure-preserving property} can return the degraded measurement to the original state despite complex degradation with the RDS concept of \textit{stability}. Our extensive experimental results corroborate the effectiveness of D$^3$GM across multiple benchmarks including a prominent application for inverse problems, magnetic resonance imaging. Code and data will be publicly available.

Diagnoses from histopathology images rely on information from both high and low resolutions of Whole Slide Images. Ultra-Resolution Cascaded Diffusion Models (URCDMs) allow for the synthesis of high-resolution images that are realistic at all magnification levels, focusing not only on fidelity but also on long-distance spatial coherency. Our model beats existing methods, improving the pFID-50k [2] score by 110.63 to 39.52 pFID-50k. Additionally, a human expert evaluation study was performed, reaching a weighted Mean Absolute Error (MAE) of 0.11 for the Lower Resolution Diffusion Models and a weighted MAE of 0.22 for the URCDM., Comment: MedNeurIPS 2023 poster

Poor performance of quantitative analysis in histopathological Whole Slide Images (WSI) has been a significant obstacle in clinical practice. Annotating large-scale WSIs manually is a demanding and time-consuming task, unlikely to yield the expected results when used for fully supervised learning systems. Rarely observed disease patterns and large differences in object scales are difficult to model through conventional patient intake. Prior methods either fall back to direct disease classification, which only requires learning a few factors per image, or report on average image segmentation performance, which is highly biased towards majority observations. Geometric image augmentation is commonly used to improve robustness for average case predictions and to enrich limited datasets. So far no method provided sampling of a realistic posterior distribution to improve stability, e.g. for the segmentation of imbalanced objects within images. Therefore, we propose a new approach, based on diffusion models, which can enrich an imbalanced dataset with plausible examples from underrepresented groups by conditioning on segmentation maps. Our method can simply expand limited clinical datasets making them suitable to train machine learning pipelines, and provides an interpretable and human-controllable way of generating histopathology images that are indistinguishable from real ones to human experts. We validate our findings on two datasets, one from the public domain and one from a Kidney Transplant study., Comment: 11 pages, 2 figures, 1 table