Understanding how the brain continuously learns and maintains memories is a challenging problem. Sensorimotor learning provided a rich quantitative framework for approaching this question. Here we build on a recent theoretical model, COIN (Heald, Lengyel, and Wolpert 2021), that has been successful in unifying motor learning paradigms, to understand how training schedules affect learning of multiple memories. A classic result in motor learning (Shea and Morgan 1979) showed that training tasks A and B in a blocked order (AAABBB) results in faster learning of A and B but poorer retention than interleaved (ABABAB) or random-order training. Explanations of these effects have been largely descriptive, characterizing the benefit of interleaving as due to (i) learning a better representation that contrasts the two memories (Kornell and Bjork 2008), or (ii) improved recall due to short-term forgetting during the other task (Lee and Magill 1983; Lu, Weiden, and Yuille 2009). Modeling the two schedules using COIN predicts higher retention for an interleaved schedule. Analyzing the internal dynamics of the COIN model revealed that poor retention for blocked training was not due to decay of the initial memory, but to an over-reliance on the history of field transitions, as opposed to the cue to infer the context for a trial. This allowed us to make the novel prediction that interleaving null-field trials between each field trial in a blocked condition should improve retention as it increases reliance on sensory cues. Empirical data in a control point paradigm suitable for multiple force-field learning (Heald, Ingram, et al. 2018) confirmed these predictions. Furthermore, varying the null field schedule, to increase the reliance on sensory cues predicted a further increase in retention, which was also supported by data. Our findings provide strong evidence for contextual inference underlying the effects of training schedules on motor learning.