STEP: Score-Based Temporal Energy for Human Pose Video Anomaly Detection

Skeleton-based Video Anomaly Detection (VAD) offers a robust, privacy-preserving solution for identifying abnormal behaviors. To model the distribution of normal static and moving poses, recent methods train Energy-Based Models (EBMs) via Denoising Score Matching (DSM). However, directly injecting noise, required for training, into raw joint coordinates creates physically impossible poses, and this structural collapse severely worsens as the temporal window expands. To address this, we introduce STEP, a simple framework that utilizes Principal Component Analysis (PCA) to project pose sequences into a compact, whitened PC-space. Learning the data density within this well-behaved PC-space ensures that the injected noise translates into physically plausible variations, which allows the model to process longer video sequences without the performance collapse of raw coordinate baselines. Additionally, to mitigate inherent pose estimation inaccuracies arising from occlusions or motion blur, we integrate a sequence-level weighting mechanism based on the estimator's confidence scores. Operating at real-time computational efficiency, our simple and lightweight framework outperforms the previous skeleton-based state-of-the-art by 12.2% (90.1% AUROC) on the challenging UBnormal dataset and achieves highly competitive results by improving on the ShanghaiTech benchmark.

Simulation-free and finite-time diffusion model

The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.

A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models

This tutorial develops diffusion models from the viewpoint of differential equations. We begin with the conditional Gaussian forward process and show that this path admits both an ordinary differential equation (ODE) representation and a stochastic differential equation (SDE) representation. Averaging the conditional process over the data distribution then yields marginalized forward ODE and SDE formulations that transport the data distribution $p_0=p_{\mathrm{data}}$ to a Gaussian prior $p_1=\mathcal{N}(0,I)$. We next derive the corresponding reverse-time dynamics, namely the reverse SDE and the reverse probability-flow ODE, both of which are governed by the marginal score $\grad\log p_t(x)$. This leads to a training objective for score estimation and shows that the standard noise-prediction objective is equivalent to score matching up to an additive constant independent of the model parameters. We then discuss sampling methods for the learned reverse dynamics, including DPM-Solver, as well as guided sampling through classifier guidance and classifier-free guidance. Finally, we compare DDPM and DDIM with the reverse SDE/ODE framework and show that they share the same training objective, while DDPM sampling corresponds to discrete reverse-SDE sampling and DDIM sampling corresponds to reverse-ODE sampling.