River-Erosion-Based Image Generation: A Feedback-Driven Framework for Iterative Visual Synthesis Through Erosion, Transport, and Deposition

Contemporary image generation methods commonly construct images through learned transformations of latent representations, iterative denoising, or direct synthesis from conditional inputs. This paper proposes River-Erosion-Based Image Generation (REGI), a mechanism-driven framework in which an image emerges through repeated erosion, transport, deposition, and feedback-dependent modification of a spatially distributed visual state. Inspired by the interaction between flowing water and evolving terrain, the framework treats visual features as mutable material whose spatial distribution can be weakened, displaced, accumulated, or reorganized over successive computational steps. Unlike conventional erosion-based terrain synthesis, the proposed framework is intended to operate on general image representations rather than being restricted to geographic height fields. A latent visual state, an auxiliary terrain-like control field, a flow field, and a material-state representation jointly determine the evolution of the generated image. Flow is estimated from the evolving control field; erosion modifies local visual material; transport redistributes displaced material; deposition incorporates transported material into receiving regions; and the resulting state changes subsequent flow. A differentiable implementation is formulated to permit optimization using reconstruction, perceptual, adversarial, and dynamical regularization objectives. The framework is specified as a research proposal, with mathematical definitions, a computational procedure, and an experimental protocol for evaluating its feasibility. No empirical superiority is claimed without implementation and controlled experiments. The principal research question is whether closed-loop erosion and material redistribution can provide useful generative behavior beyond static flow guidance, conventional local-update systems, and existing iterative image-generation methods.