English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The aim of this short note is to show that Denoising Diffusion ProbabilisticModel DDPM, a non-homogeneous discrete-time Markov process, can be representedby a time-homogeneous continuous-time Markov process observed at non-uniformlysampled discrete times. Surprisingly, this continuous-time Markov process isthe well-known and well-studied Ornstein-Ohlenbeck (OU) process, which wasdeveloped in 1930's for studying Brownian particles in Harmonic potentials. Weestablish the formal equivalence between DDPM and the OU process using itsanalytical solution. We further demonstrate that the design problem of thenoise scheduler for non-homogeneous DDPM is equivalent to designing observationtimes for the OU process. We present several heuristic designs for observationtimes based on principled quantities such as auto-variance and FisherInformation and connect them to ad hoc noise schedules for DDPM. Interestingly,we show that the Fisher-Information-motivated schedule corresponds exactly thecosine schedule, which was developed without any theoretical foundation but isthe current state-of-the-art noise schedule.

Using Ornstein-Uhlenbeck Process to understand Denoising Diffusion Probabilistic Model and its Noise Schedules