The current Von-Neumann architecture cannot support emerging applications in artificial intelligence, necessitating a new computing paradigm that can solve complex tasks. Memristor-based near-memory computing demonstrates the potential beyond Von-Neumann computers. However, due to device limitations, memristor-based hardware with bulky peripheral circuits cannot handle complex tasks and is sensitive to noise. In this study, we leverage the physical stochasticity of a diffusive device and the inherent parallelism of the crossbar structure to implement a true stochastic Bayesian machine based on an Au/Ag/Al₂O₃/Pt/Ti memristor crossbar array circuit. The proposed system supports long probabilistic sequence inference with superior soft-error robustness and enables probabilistic hardware to handle high-feature tasks such as image recognition for the first time. We have constructed a diffusive memristor device with the corresponding compact model and measured the signal-transmission characteristics of the crossbar array prototype circuit, revealing severe signal distortion due to parasitic effects. Moreover, we propose a signal-reconstruction method that effectively improves the performance of Bayesian machine circuits. Our work points to new directions for exploring circuit design and large-scale integration methods in probabilistic computing hardware.