We study the problem of modeling a population of agents pursuing unknown goals subject to unknown computational constraints. In standard models of bounded rationality, sub-optimal decision-making is simulated by adding homoscedastic noise to optimal decisions rather than actually simulating constrained inference. In this work, we introduce a latent inference budget model (L-IBM) that models these constraints explicitly, via a latent variable (inferred jointly with a model of agents’ goals) that controls the runtime of an iterative inference algorithm. L-IBMs make it possible to learn agent models using data from diverse populations of suboptimal actors. In three modeling tasks—inferring navigation goals from routes, inferring communicative intents from human utterances, and predicting next moves in human chess games—we show that L-IBMs match or outperforms Boltzmann models of decision-making under uncertainty. Moreover, the inferred inference budgets are themselves meaningful, efficient to compute, and correlated with measures of player skill, partner skill and task difficulty.