Denoising Network Parameterisation in CTMC

This is achieved by formulating the forward noising process and corresponding reverse time generative process as Continuous Time Markov Chains (CTMCs). The model can be efficiently trained using a continuous time version of the ELBO. Here is a detailed explanation of the denoising‐network / reverse‐process architecture in the paper A Continuous Time Framework for Discrete Denoising Models by Andrew Campbell et al (NeurIPS 2022) — including how the continuous‐time Markov chain (CTMC) forward process is defined, how the reverse/denoising network is trained, and how sampling (generation) proceeds. I’ll also provide the training and sampling pseudocode/algorithm sketch.

for each minibatch:
   sample x0 ~ p_data
   sample t ~ Uniform(0, T)
   sample xt ~ q_{t|0}(· | x0)
   compute network output p_theta(x0 | xt, t)
   compute loss term L(theta) using formula involving R_t and p_theta
   update theta by gradient descent