Generative methods have reached a level of quality that is almost indistinguishable from real data. However, while individual samples may appear unique, generative models often exhibit limitations in covering the full data distribution. Unlike quality issues, diversity problems within generative models are not easily detected by simply observing single images or generated datasets, which means we need a specific measure to assess the diversity of these models. In this paper, we draw attention to the current lack of diversity in generative models and the inability of common metrics to measure this. We achieve this by framing diversity as an image retrieval problem, where we measure how many real images can be retrieved using synthetic data as queries. This yields the Image Retrieval Score (IRS), an interpretable, hyperparameter-free metric that quantifies the diversity of a generative model’s output. IRS requires only a subset of synthetic samples and provides a statistical measure of confidence. Our experiments indicate that current feature extractors commonly used in generative model assessment are inadequate for evaluating diversity effectively. Consequently, we perform an extensive search for the best feature extractors to assess diversity. Evaluation reveals that current diffusion models converge to limited subsets of the real distribution, with no current state-of-the-art models superpassing 77% of the diversity of the training data. To address this limitation, we introduce Diversity-Aware Diffusion Models (DiADM), a novel approach that improves diversity of unconditional diffusion models without loss of image quality. We do this by disentangling diversity from image quality by using a diversity aware module that uses pseudo-unconditional features as input. We provide a Python package offering unified feature extraction and metric computation to further facilitate the evaluation of generative models https://github.com/MischaD/beyondfid.

As deep learning models continue to scale in complexity and data size, reducing storage and training costs has become increasingly important. Dataset distillation addresses this challenge by synthesizing a small set of synthetic samples that effectively substitute for the original dataset in downstream tasks. Existing approaches typically rely on matching gradients or features either in pixel space or in the latent space of a pretrained generative model. We propose a novel stochastic distillation method that models the joint distribution of latent features using a low-rank multivariate normal distribution, parameterized by a lightweight neural network. This formulation captures spatial correlations in the feature space, which are then projected into class probability space to generate more diverse and informative predictions. The proposed module integrates seamlessly with existing distillation pipelines. Our method achieves state-of-the-art cross-architecture results, improving test accuracy by up to 7.47% in gradient matching and 35.71% in distribution matching over baselines. • Introduce SLFD, a framework that distills data with stochastic latent features. • Model spatial correlations using a low-rank multivariate distribution. • Achieve robust performance on high-resolution ImageNet-1K subsets. • Demonstrate applicability to medical imaging with strong results.

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 Dynamics-aware SDE Diffusion Generative Model (D^3GM). The Measure-preserving property can return the degraded measurement to the original state despite complex degradation with the RDS concept of stability. Our extensive experimental results corroborate the effectiveness of D^3GM across multiple benchmarks including a prominent application for inverse problems, magnetic resonance imaging.