Recent progress of video diffusion models have enabled extensive simulation of the physical world. While simulation with hand object interaction has been less explored. We propose DexSIM, a dexterous simulation framework for simulating dexterous manipulation in real-time. While previous works utilizing video diffusion and 3D reconstruction focus on navigation, dexterous manipulation has been limited while it has extensive applications for creating interactive experiences with the simulated world and for generating synthetic data for robotics. Existing methods lack real-time interactivity and long-term spatial consistency and memory. We propose a 2-stage training framework for DexSIM. First we train a bi-directional video diffusion model by jointly embedding the hand action trajectory and video in a unified feature space. We utilize gaussian heatmap hand encoding for more accurate hand representation. Then we conduct a roll-out based autoregressive training with updated spatial cache as attention sink for spatial memory, which improves long-term consistency and 3D aware dexterous manipulation simulation. DexSIM outperforms the baseline on pixel and semantic similarity, motion fidelity, and hand projection accuracy. It also allows new applications such as hand motion transfer and runs at 15.24 FPS real-time interactivity.