Cheng Ouyang

Zhe Li, Sarah Cechnicka, Cheng Ouyang et al.

As deep learning models grow in complexity and the volume of training data increases, reducing storage and computational costs becomes increasingly important. Dataset distillation addresses this challenge by synthesizing a compact set of synthetic data that can effectively replace the original dataset in downstream classification tasks. While existing methods typically rely on mapping data from pixel space to the latent space of a generative model, we propose a novel stochastic approach that models the joint distribution of latent features. This allows our method to better capture spatial structures and produce diverse synthetic samples, which benefits model training. Specifically, we introduce a low-rank multivariate normal distribution parameterized by a lightweight network. This design maintains low computational complexity and is compatible with various matching networks used in dataset distillation. After distillation, synthetic images are generated by feeding the learned latent features into a pretrained generator. These synthetic images are then used to train classification models, and performance is evaluated on real test set. We validate our method on several benchmarks, including ImageNet subsets, CIFAR-10, and the MedMNIST histopathological dataset. Our approach achieves state-of-the-art cross architecture performance across a range of backbone architectures, demonstrating its generality and effectiveness.

Weitong Zhang, Chengqi Zang, Liu Li et al.

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.