InJecteD: Analyzing Trajectories and Drift Dynamics in Denoising Diffusion Probabilistic Models for 2D Point Cloud Generation

Abstract

This work introduces InJecteD, a framework for interpreting Denoising Diffusion Probabilistic Models (DDPMs) by analyzing sample trajectories during the denoising process of 2D point cloud generation. We apply this framework to three datasets from the Datasaurus Dozen — bullseye, dino, and circle — using a simplified DDPM architecture with customizable input and time embeddings. Our approach quantifies trajectory properties, including displacement, velocity, clustering, and drift field dynamics, using statistical metrics such as Wasserstein distance and cosine similarity. By enhancing model transparency, InJecteD supports human-AI collaboration by enabling practitioners to debug and refine generative models. Experiments reveal distinct denoising phases: initial noise exploration, rapid shape formation, and final refinement, with dataset-specific behaviors (e.g., bullseye’s concentric convergence vs. dino’s complex contour formation). We evaluate four model configurations, varying embeddings and noise schedules, demonstrating that Fourier-based embeddings improve trajectory stability and reconstruction quality. The code and dataset are available at https://github.com/s4nyam/InJecteD.