We present the Generalized Spatial Propagation Network (GSPN), a new attention mechanism optimized for vision tasks that inherently captures 2D spatial structures. Existing attention models, including transformers, linear attention, and state-space models like Mamba, process multi-dimensional data as 1D sequences, compromising spatial coherence and efficiency. GSPN overcomes these limitations by directly operating on spatially coherent image data and forming dense pairwise connections through a line-scan approach. Central to GSPN is the Stability-Context Condition, which ensures stable, context-aware propagation across 2D sequences and reduces the effective sequence length to $\sqrt{N}$ for a square map with N elements, significantly enhancing computational efficiency. With learnable, input-dependent weights and no reliance on positional embeddings, GSPN achieves superior spatial fidelity and state-of-the-art performance in vision tasks, including ImageNet classification, class-guided image generation, and text-to-image generation. Notably, GSPN accelerates SD-XL with softmax-attention by over $84\times$ when generating 16K images.

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a purely probabilistic model. We show the model's competitiveness on scarce supervision scenarios, handling missing data, and graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.