Geometric Time Score Estimators: Bridging Self-Predictive Representations and Generative Occupancy Models For Reinforcement Learning

The temporal lag between actions and their long-term consequences makes credit assignment a challenge when learning goal-directed behaviors from data. Generative world models capture the distribution of future states an agent may visit, indicating that they have captured temporal information. How can that temporal information be extracted to perform credit assignment? In this paper, we formalize how the temporal information stored in world models encodes the underlying geometry of the world. Leveraging optimal transport, we extract this geometry from a learned model of the occupancy measure into a reward function that captures goal-reaching information. Our resulting method, Occupancy Reward Shaping, largely mitigates the problem of credit assignment in sparse reward settings. ORS provably does not alter the optimal policy, yet empirically improves performance by 2.2x across 13 diverse long-horizon locomotion and manipulation tasks. Moreover, we demonstrate the effectiveness of ORS in the real world for controlling nuclear fusion on 3 Tokamak control tasks. Code: https://github.com/aravindvenu7/occupancy_reward_shaping; Website: https://aravindvenu7.github.io/website/ors/

Future 3D semantic occupancy forecasting and motion planning are central to autonomous driving, as they require models to reason about how surrounding scenes evolve and how the ego vehicle should act. Existing occupancy world models commonly discretize scenes into latent embeddings, volumetric features, or quantized tokens, and forecast future states through fixed-step autoregressive generation. This limits temporal flexibility, obscures scene evolution, accumulates errors over long horizons, and poorly matches the continuous-time dynamics of real driving scenes. We propose GEM, a Gaussian Evolution Model for non-autoregressive occupancy world modeling, where driving scenes are represented as explicit continuous 4D Gaussian primitives with learned dynamics. Instead of rolling out future occupancy states step by step, GEM directly queries the Gaussian world representation at arbitrary timestamps and splats the corresponding conditional 3D Gaussians into semantic occupancy volumes. This enables efficient forecasting over the full horizon while retaining a compact and interpretable scene representation. By decoupling spatial geometry, temporal support, and primitive motion, GEM makes the predicted world easier to inspect, as each primitive's evolution can be followed continuously over time. The same representation also supports motion planning by predicting future ego trajectories from the learned Gaussian world. Extensive experiments show that GEM achieves state-of-the-art future semantic occupancy forecasting and strong motion planning performance, while providing flexible temporal querying.

The growing interest in behavior foundation models, combined with recent advancements in generative modeling, has led to an appealing recipe for reinforcement learning from unlabeled data: pre-train a generative model to model occupancies, i.e., discounted state visitations, on reward-free trajectories, such that a policy can be easily extracted once a small reward-labeled dataset becomes available. We decompose this recipe along three axes: (i) the degree to which the multi-modal structure of occupancies must be captured, (ii) the class of generative model, and (iii) the method used for policy extraction. Along each axis, we consider existing choices, propose simpler alternatives, and validate each decision experimentally. This analysis culminates in a novel, streamlined method that leverages drifting, a modern one-step generative sampler, to model the occupancy. We show that this enables policy extraction via direct differentiation through the occupancy model, and bypasses the need for critic distillation. Overall, we observe that this nimble setup leads to improvements in performance on standard benchmarks.