Large language models (LLMs) have demonstrated strong performance and rapid progress in a wide range of medical reasoning tasks.However, their sequential autoregressive decoding forces inherently parallel clinical reasoning, such as differential diagnosis, into a single linear reasoning path, limiting both efficiency and reliability for complex medical problems.To address this, we propose MedVerse, a reasoning framework for complex medical inference that reformulates medical reasoning as a parallelizable directed acyclic graph (DAG) process based on Petri Net theory.The framework adopts a full-stack design across data, model architecture, and system execution.For data creation, we introduce the MedVerse Curator, an automated pipeline that synthesizes knowledge-grounded medical reasoning path and transforms them into Petri Net–structured representations.At the architectural level, we propose a topology-aware attention mechanism with adaptive position indices that supports parallel reasoning while preserving logical consistency.Systematically, we develop a customized inference engine that supports parallel execution without additional overhead.Empirical evaluations show that MedVerse improves strong general-purpose LLMs by up to 8.9%. Compared to specialized medical LLMs, MedVerse achieves comparable performance with improved clinical reliability, while delivering a 1.3× reduction in inference latency and a 1.7× increase in generation throughput, enabled by its parallel decoding capability.