Reliable training of a clean-null conditional denoiser

Develop a conditional, autoregressively trained diffusion denoiser that reliably converges to a regime in which the probability-flow ODE encoder maps pre-change observations to an exact standard Gaussian latent distribution, thereby supporting the paper’s exact-null calibration and detection guarantees.

Background

The proposed change-detection procedure assumes that a conditional probability-flow ODE diffusion model, trained on pre-change data with a frozen context, produces latent variables distributed as $\mathcal N(0,I)$ under the null hypothesis. This assumption is essential because the MMD null distribution, likelihood-ratio construction, and false-alarm calibration all depend on the latent reference distribution being correct.

The MNIST experiment demonstrates that this condition may fail in practice: DDIM inversion produced latent codes with mean per-dimension variance substantially below one. The paper therefore identifies reliable convergence of the autoregressive denoiser to a genuinely clean null as the principal unresolved technical issue.