There is a growing gap between the impressive results of deep image
generative models and classical algorithms that offer theoretical guarantees.
The former suffer from mode collapse or memorization issues, limiting their
application to scientific data. The latter require restrictive assumptions such
as log-concavity to escape the curse of dimensionality. We partially bridge
this gap by introducing conditionally strongly log-concave (CSLC) models, which
factorize the data distribution into a product of conditional probability
distributions that are strongly log-concave. This factorization is obtained
with orthogonal projectors adapted to the data distribution. It leads to
efficient parameter estimation and sampling algorithms, with theoretical
guarantees, although the data distribution is not globally log-concave. We show
that several challenging multiscale processes are conditionally log-concave
using wavelet packet orthogonal projectors. Numerical results are shown for
physical fields such as the $\varphi^4$ model and weak lensing convergence maps
with higher resolution than in previous works.

介绍了条件强对数凹模型的概念，该模型将数据分布因子化为强对数凹条件概率分布的乘积，并使用适应于数据分布的正交投影器来实现因子化，从而实现了有效的参数估计和抽样算法，并在物理字段等多个领域展示了该模型的实用性。