Diffusion Models are probabilistic generative model for generating high-quality novel, never-before-seen, samples. It's based on a diffusion process, a concept from physics that describes the dispersion of particles over time. Typical generative diffusion models rely on a Gaussian diffusion process for training the reverse-time transformations, which is the vessel for generating samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce “Blackout Diffusion”, which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how we should understand/interpret diffusion models, which we will discuss.