The Tree of Diffusion Life: Evolutionary Embeddings to Understand the Generation Process of Diffusion Models

Diffusion models generate high-quality samples by corrupting data with Gaussian noise and iteratively reconstructing it with deep learning, slowly transforming noisy images into refined outputs. Understanding this data evolution is important for interpretability but is complex due to its high-dimensional evolutionary nature. While traditional dimensionality reduction methods like t-distributed stochastic neighborhood embedding (t-SNE) aid in understanding high-dimensional spaces, they neglect evolutionary structure preservation. Hence, we propose Tree of Diffusion Life (TDL), a method to understand data evolution in the generative process of diffusion models. TDL samples a diffusion model's generative space via instances with varying prompts and employs image encoders to extract semantic meaning from these samples, projecting them to an intermediate space. It employs a novel evolutionary embedding algorithm that explicitly encodes the iterations while preserving the high-dimensional relations, facilitating the visualization of data evolution. This embedding leverages three metrics: a standard t-SNE loss to group semantically similar elements, a displacement loss to group elements from the same iteration step, and an instance alignment loss to align elements of the same instance across iterations. We present rectilinear and radial layouts to represent iterations, enabling comprehensive exploration. We assess various feature extractors and highlight TDL's potential with prominent diffusion models like GLIDE and Stable Diffusion with different prompt sets. TDL simplifies understanding data evolution within diffusion models, offering valuable insights into their functioning.

ParaDime: A Framework for Parametric Dimensionality Reduction

ParaDime is a framework for parametric dimensionality reduction (DR). In parametric DR, neural networks are trained to embed high-dimensional data items in a low-dimensional space while minimizing an objective function. ParaDime builds on the idea that the objective functions of several modern DR techniques result from transformed inter-item relationships. It provides a common interface to specify the way these relations and transformations are computed and how they are used within the losses that govern the training process. Through this interface, ParaDime unifies parametric versions of DR techniques such as metric MDS, t-SNE, and UMAP. Furthermore, it allows users to fully customize each aspect of the DR process. We show how this ease of customization makes ParaDime suitable for experimenting with interesting techniques, such as hybrid classification/embedding models or supervised DR, which opens up new possibilities for visualizing high-dimensional data.