Progress estimators play an essential role in providing dense reward signals for reinforcement learning in robotic manipulation, but accurately assessing task progress can be much challenging. Existing methods heavily rely on expert data and naively assume that all actions within a demonstration contribute to task success. This assumption often breaks down in real-world scenarios, especially in high-precision manipulation, where subtle geometric errors can lead to task failure. Therefore, these methods can erroneously interpret human mistakes as meaningful progress, further corrupting progress learning. We argue that a key limitation is the lack of a global prior regarding task evaluation criteria, which is crucial for distinguishing meaningful progress from human mistakes. To this end, we propose PRIME, a novel progress estimator capable of learning precise progress estimation from imprecise demonstrations by aggregating experience across trajectories. PRIME constructs a weighted graph over observed states, connecting states across trajectories based on spatial proximity and visual consistency. Edge weights encode spatial distances as transition costs, and shortest-path search approximates the geodesic distance to success. Changes in this distance naturally distinguish advancement, stagnation, and setbacks without assuming monotonic progress over time. Extensive experiments in both simulation and real world on precise manipulation tasks show that PRIME is consistently effective across diverse tasks, and robust to data with varying degrees of suboptimality. Notably, the advantage of PRIME gets more pronounced in higher-precision scenarios, yielding up to a
5× improvement in policy success rate over the SFT baselines on charger insertion.