Theoretical work on reproducibility of scientific claims has hitherto focused on hypothesis testing as the desired mode of statistical inference. Focusing on hypothesis testing, however, poses a challenge to identify salient properties of the scientific process related to reproducibility, especially for fields that progress by building, comparing, selecting, and re-building models. We build a model-centric meta-scientific framework in which scientific discovery progresses by confirming models proposed in idealized experiments. In a temporal stochastic process of scientific discovery, we define scientists with diverse research strategies who search the true model generating the data. When there is no replication in the system, the structure of scientific discovery is a particularly simple Markov chain. We analyze the effect of diversity of research strategies in the scientific community and the complexity of the true model on the time spent at each model, the mean first time to hit the true model and staying with the true model, and the rate of reproducibility given a true model. Inclusion of replication in the system breaks the Markov property and fundamentally alters the structure of scientific discovery. In this case, we analyze aforementioned properties of scientific discovery by an agent-based model. In our system, the seeming paradox of scientific progress despite irreproducibility persists even in the absence of questionable research practices and incentive structures, as the rate of reproducibility and scientific discovery of the truth are uncorrelated. We explain this seeming paradox by a combination of research strategies in the population and the state of truth. Further, we find that innovation speeds up the discovery of truth by making otherwise inaccessible, possibly true models visible to the scientific population. We also show that epistemic diversity in the scientific population optimizes across a range of desirable properties of scientific discovery.