Recent developments in diffusion models have advanced conditioned image generation, yet they struggle with reconstructing out-of-distribution (OOD) images, such as unseen tumors, causing 'image hallucination' and risking misdiagnosis. We hypothesize such hallucinations result from local OOD regions in the conditional images. By partitioning the OOD region and conducting separate generations, hallucinations can be alleviated, and we verify this with motivational studies in several applications. From this, we propose a training-free diffusion framework that reduces hallucination by performing multiple \textit{Local Diffusion} processes. Our approach involves OOD estimation followed by two diffusion modules: a 'branching' module for local image generations from OOD estimations, and a 'fusion' module to integrate these predictions into a full image cohesively. These modules adapt to each testing dataset by updating an auxiliary classifier. Our evaluation shows our method improves baseline models quantitatively and qualitatively across different datasets. It also works well with various pre-trained diffusion models as a plug-and-play option.