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

arXiv: https://arxiv.org/abs/2509.12239 · HTML: https://mlsanity.com/paper/2509.12239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 9 of 9)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [DragDiffusion: Harnessing Diffusion Models for Interactive Point-based Image Editing](https://mlsanity.com/paper/2306.14435/) (2023)
- [Point Cloud Diffusion Models for Automatic Implant Generation](https://mlsanity.com/paper/2303.08061/) (2023)
- [Explaining generative diffusion models via visual analysis for interpretable decision-making process](https://mlsanity.com/paper/2402.10404/) (2024)
- [Neural Point Cloud Diffusion for Disentangled 3D Shape and Appearance Generation](https://mlsanity.com/paper/2312.14124/) (2023)
- ['Explaining RL Decisions with Trajectories': A Reproducibility Study](https://mlsanity.com/paper/2411.07200/) (2024)

## Abstract (arXiv)

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 example, bullseyes concentric convergence vs. dinos complex contour formation. We evaluate four model configurations, varying embeddings and noise schedules, demonstrating that Fourier based embeddings improve trajectory stability and reconstruction quality