Deep Active Inference with Diffusion Policy and Multiple Timescale World Model for Real-World Exploration and Navigation

The diffusion based robot navigation world models are typically trained using parallel supervision, while autoregressive inference is employed during path planning. This results in a distribution shift between training and inference, which destabilizes the performance over long-horizon prediction. We propose AR Forcing, an autoregressive training strategy, which integrates the standard diffusion loss into the autoregressive training loop. At each step, the model uses its own predictions to update the context and optimize the single step noise prediction objective, thereby explicitly exposing the model to the inference state distribution during training. Our method does not require additional discriminators or distribution-matching losses, retains the original diffusion framework and sampler, and is easy to integrate. Experiments on multi-domain navigation datasets (RECON, SCAND, HuRoN, TartanDrive) show that compared with strong baselines, AR Forcing improved the consistency of generated images during long-horizon navigation and the accuracy of predicted trajectories, enhancing robustness of the model in complex known and unknown environments. We will release the code soon.

Lifelong embodied navigation in dynamic environments requires robots to form persistent scene understanding from fragmentary observations, which remains difficult for existing methods that rely on explicit maps or scene graphs and struggle to generalize beyond structured settings. We propose AllDayNav, a lifelong self-learning navigation framework that implicitly encodes scene dynamics into the billion-scale parameters of a large model via reinforcement learning, powered by a self-evolving multimodal memory that maintains and updates visual keyframes, semantic descriptions, and temporal context while autonomously generating open-vocabulary instructions, image goals, and structured rewards. Experiments in both synthetic and real-world environments across cross-room, cross-episode, and cross-task scenarios show that AllDayNav achieves success rates approaching $100\%$ and consistently surpasses strong map-based, VLM, and RL baselines in path efficiency and robustness, demonstrating implicit, memory-driven reinforcement learning as a scalable alternative to explicit mapping for reliable lifelong navigation.

Autonomous navigation in dense and highly dynamic environments requires both physically feasible control and low-latency replanning. Optimization-based methods such as Model Predictive Control (MPC) explicitly handle robot kinematics and safety constraints, but repeated nonlinear optimization can limit real-time responsiveness. Deterministic behavior-cloning policies enable efficient inference but may fail to represent multimodal avoidance behaviors, whereas diffusion policies capture multimodality at the cost of time-consuming iterative denoising. We propose PIER-Flow (Physics-Informed Efficient Rectified Flow), a lightweight navigation policy for mobile robots. By distilling an MPC expert into a continuous-time Ordinary Differential Equation (ODE), PIER-Flow achieves single-step action generation through parallel latent sampling and lightweight feasibility selection. We introduce a physics-informed training objective to enforce kinematic consistency, paired with an asynchronous action chunking architecture for robust sim-to-real deployment. Extensive simulations demonstrate that PIER-Flow achieves a 98.85% success rate and zero collisions, with an average inference of $\sim$1.29 ms, which accelerates planning by 37.2$\times$ compared to MPC and over 800$\times$ against standard diffusion models. Crucially, real-world deployment on a resource-constrained edge computer further achieves an approximately stable inference latency of $\sim$5.3 ms, avoiding the latency spikes and freezing events observed with planning baselines.