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Diffusion models are inspired by non-equilibrium thermodynamics. They define a Markov chain of diffusion steps to slowly add random noise to data, then learn to reverse the diffusion process to construct desired data samples from the noise. Forward Diffusion Suppose a multi-variate random variable $\mathbf{X}=[X_1,\dots,X_L] \sim q(\bm{x})$, where $L=H*W*3$ and $\bm{x}=[x_1,\dots,x_L]$, i.e., the observed image, $\bm{x}_0 \in \mathbb{R}^{L}$, is sampled from the underlying true distribution $q(\bm{x})$. Starting from the observation $\bm{x}_0$, forward diffusion progressively adds gaussian noise sampled from $\mathcal{N}(\bm{\mu}_t,\bm{\Sigma}_t)$ in $T$ steps, producing a sequence of noisy samples $\bm{x}_1,\dots,\bm{x}_T$....