Summary: Objective In a denoising diffusion model, given
an input $\mathbf x^0$ drawn from a complicated and unknown distribution $q(\mathbf x^0)$, we find
a latent space with a simple and manageable distribution, e.g., normal distribution, and the transformations from $\mathbf x^0$ to $\mathbf x^n$, as well as the transformations from $\mathbf x^n$ to $\mathbf x^0$. An Example For example, with $N=5$, the forward process is
flowchart LR x0 --> x1 --> x2 --> x3 --> x4 --> x5 and the reverse process is
flowchart LR x5 --> x4 --> x3 --> x2 --> x1 --> x0 The joint distribution we are searching for is

Summary: Boltzmann machine is much like a spin glass model in physics. In short words, Boltzmann machine is a machine that has nodes that can take values, and the nodes are connected through some weight. It is just like any other neual nets but with complications and theoretical implications.