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I have read several papers about diffusion models in the context of deep learning. especially this one

As explained in the paper, by learning the score function $(\nabla \log(p_t(x)))$, probability flow ode trajectory would uniquely map any data point in data distribution (let's say images) to a point in multivariate gaussian distribution of the same dimension, as shown in Figure 2 in the paper. I have several questions:

  1. We know that we can draw a random a sample from the gaussian distribution and the reverse SDE would generate sample from the data distribution, in this case a realistic image. Is that also true for the reverse ODE?

  2. Can we say ODE trajectory is a bijective mapping from the data distribution to the gaussian distribution?

  3. Can we say in such gaussian distribution every element (dimension) is independent of the others? The motivation for this question is, I want to find a mapping or a new representation of my data, in which every element is independent of the others (some sort of disentangled representation, but interpretability doesn't matter). Can such mapping replace the ICA algorithm?

enter image description here

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    $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented Jul 5 at 7:55

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