  Generative models based on diffusion have become the state of the art in the
last few years, notably for image generation. Here, we analyse them in the
high-dimensional limit, where data are formed by a very large number of
variables. We use methods from statistical physics and focus on two
well-controlled high-dimensional cases: a Gaussian model and the Curie-Weiss
model of ferromagnetism. In the latter case, we highlight the mechanism of
symmetry breaking in the inverse diffusion, and point out that, in order to
reconstruct the relative asymmetry of the two low-temperature states, and thus
to obtain the correct probability weights, one needs a database with a number
of points much larger than the dimension of each data point. We characterize
the scaling laws in the number of data and in the number of dimensions for an
efficient generation.
