We present Spanning Tree Autoregressive (STAR) modeling, which can incorporate prior knowledge of images, such as center bias and locality, to maintain sampling performance while also providing sufficiently flexible sequence orders to accommodate image editing at inference time. Approaches that expose conventional autoregressive (AR) models in visual generation to arbitrary sequence orders via random permutation suffer from degraded sampling performance or compromise the flexibility in sequence order choice at inference time. Instead, STAR utilizes traversal orders of uniform spanning trees in a lattice defined by the positions of image patches. Traversal orders are obtained via breadth-first search, allowing us to efficiently construct a spanning tree via rejection sampling whose traversal order ensures that the connected partial observation of the image appears as a prefix for native image inpainting support. Through the tailored yet structured sequence order randomization strategy, STAR preserves the capability of postfix completion while maintaining sampling performance, without any significant changes to the model architecture widely adopted in language AR modeling.

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