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.

翻译：我们提出了一种自动定义并学习具有问题特定结构的深度生成模型框架。我们致力于处理传统上由排序、数独约束求解和矩阵分解等算法解决的任务领域。具体而言，我们训练具有适应问题规范架构的扩散模型。该问题规范应包含描述变量间关系的图模型，并常得益于子计算的显式表示。置换不变性也可加以利用。通过在多样化实验中的验证，我们在训练时间和最终精度方面改进了问题维度与模型性能之间的规模关联。