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First, we notice that It implies that and, so, we can reparametrise the model by defining so that With this new parametrisation, we no longer learn a model that represent the mean of the reverse process but a model that represent the noise that has been added into x_0 to get x_t

Indeed, we already saw that and we can show that where The KL divergence between 2 gaussian distributions having a closed form, we will see in the next section that this upper bound defines a very tractable loss function to be minimised for the training process

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