Stochastic modeling is an essential component of the quantitative sciences, with hidden Markov models (HMMs) often playing a central role. Concurrently, the rise of quantum technologies promises a host of advantages in computational problems, typically in terms of the scaling of requisite resources such as time and memory. HMMs are no exception to this, with recent results highlighting quantum implementations of deterministic HMMs exhibiting superior memory and thermal efficiency relative to their classical counterparts. In many contexts, however, nondeterministic HMMs are viable alternatives; compared to them, the advantages of current quantum implementations do not always hold. Here, we provide a systematic prescription for constructing quantum implementations of nondeterministic HMMs that reestablish the quantum advantages against this broader class. Crucially, we show that whenever the classical implementation suffers from thermal dissipation due to its need to process information in a time-local manner, our quantum implementations will both mitigate some of this dissipation and achieve an advantage in memory compression.