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Your mentioned DDPM is Ho et al's Denoising Diffusion Probabilistic Models (2020), and as you rightly quoted that the reparameterization of the forward process posterior variational mean $\mathbf{\mu_ … Therefore once it's trained successfully as implemented by the paper's Algorithm 1, DDPM captures all the crucial noises at each time step during the reverse denoise diffusion process to reconstruct the …

It seems you've already understood up to the step of the exact conditional probability of the reverse diffusion process $q(\mathbf{x}_{t-1}|\mathbf{x}_t, \mathbf{x}_0)$ which is proportional to the exponential … of your mentioned 2nd order polynomial with 3 terms per Bayes theorem along with conditional probabilities defined in the forward diffusion process with some mentioned nice property. …

So the objective is to find the parameters of the neural network to minimize expectation of the sum of these KL divergences wrt the forward diffusion process's variational distribution $q(\mathbf{x}_{1 … tilde\mu}_t$ as posterior means do not concern the same (Gaussian) distribution, but according to the form of the above $l_2$ loss, so long as they're close, the ELBO optimization as inference of the diffusion …

Your own cited blog explains the nice property to avoid posterior collapse in DDGMs simply due to the design of diffusion models. … Before, we used normal distributions parameterized by DNNs but now we formulate them as the following Gaussian diffusion process (Sohl-Dickstein et al., 2015)... …

From your reference "Understanding Diffusion Models: A Unified Perspective", the ground truth claims for score function appear in places like: The score model can be optimized by minimizing the Fisher …

The case for diffusion models' ELBO optimization is similar. …