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

In reinforcement learning (RL), temporal reasoning is essential for estimating the density of future outcomes under a policy's occupancy measure. While self-predictive representations have been a dominant paradigm for occupancy density estimation, we find that they yield surprisingly poor estimates. On the other hand, generative occupancy models can produce remarkably accurate samples from the occupancy measure. Yet, they cannot easily recover occupancy densities, limiting their use for control despite their expressivity. In this paper, we propose $\text{Geometric Time Score Estimators (GTSE)}$, a framework that bridges the two paradigms by learning occupancy density estimators along probability paths. We analyze how GTSE implicitly induces better occupancy estimators through improved representation learning and show how to directly extract self-predictive representations from this framework. Through experiments across several locomotion and manipulation tasks, we show that GTSE improves performance over state-of-the-art methods by $2\times$ to $6\times$ in goal-conditioned RL settings, and that the representations learned using our framework transfer effectively to downstream RL tasks.