Discrete generative diffusion models without stochastic differential equations: a tensor network approach

The use of DMs has grown to become the method of choice for image generation. A central problem in machine learning (ML) is how to train a model to efficiently generate samples from a The standard formulation of DMs in terms of Brownian probability distribution of interest [1, 2]. Two typical motion and stochastic differential equations presents scenarios are where this target distribution is only known three main challenges. The first one is the estimation through sampled data, or where relative probabilities are of the denoising SDE via the score [9], which has to be known but the overall normalisation is not [3]. There learned as a function over the whole domain of the target are many ML strategies to address this problem, a subset probability from sparse and high dimensional training of which is based on the idea that a model can be data. The second one is how to resolve the "mismatch trained to transform a "noise" distribution (such as a in time" [12]: under Brownian dynamics the mapping Gaussian) into a non-trivial distribution of interest over from the target distribution to a noisy Gaussian happens the same domain, in such a way that (easily extractable) only asymptotically, while in practice the denoising noise samples from the first distribution can be transformed process is run over finite times, thus incurring in a reconstruction into (difficult to generate) samples of the target error. The third challenge is how to precisely one. This is the general approach of both "normalising estimate the likelihood of generated configurations from flows" [4-6], and of the so-called diffusion models [7-10] the learned score.