Probability Diffusion with Neighboring Probability Correction: A Spatially Coupled Framework for Image Generation

Image generation requires the progressive construction of spatially coherent visual patterns from random initial states. Diffusion models accomplish this by learning reverse transitions from noisy images, while probabilistic graphical models represent dependencies among neighboring variables. These approaches establish the importance of probabilistic modeling and spatial interaction, but they leave room to investigate alternative mechanisms for explicitly correcting local pixel distributions during generation. This paper proposes Probability Diffusion with Neighboring Probability Correction (PDNPC), a framework in which each spatial position maintains a probability distribution over candidate pixel values, and these distributions are iteratively adjusted through neighborhood-dependent compatibility messages and a learned global image prior. Rather than independently sampling each pixel from its initial distribution, PDNPC updates local distributions according to both pixel-specific evidence and the probabilistic relationships between neighboring positions. The framework introduces a probability diffusion state, a neighborhood correction operator, a compatibility-based joint distribution, and an uncertainty-sensitive correction schedule. To avoid the degeneration associated with excessive local agreement, the method incorporates data-dependent compatibility, temperature-controlled updates, and a learned generative prior. The paper presents a mathematical formulation, an iterative generation algorithm, a possible training objective, and an experimental protocol. Importantly, diffusion-based image generation, autoregressive pixel modeling, and spatial probabilistic dependencies are established research areas. The proposed contribution is therefore a specific, testable framework for integrating iterative neighborhood probability correction with a learned image-generation process, rather than a claim that these individual principles are new. No experimental results are claimed.