We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

翻译：我们提出了一种框架，用于自动定义和学习具有特定问题结构的深度生成模型。我们处理那些传统上由算法（如排序、数独约束满足及矩阵分解）解决的问题领域。具体而言，我们训练了扩散模型，其架构针对问题描述进行了定制。该问题描述应包含描述变量间关系的图形模型，并且通常受益于子计算的显式表示。排列不变性也可被利用。在一系列多样化的实验中，我们改进了问题维度与模型性能之间的缩放关系，体现在训练时间和最终准确率两方面。我们的代码可在 https://github.com/plai-group/gsdm 获取。