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Abstract: Facilitated by advancements in conflict event databases, studies have moved towards predicting armed conflict and understanding its determinants subnationally. However, existing statistical models do not analyze nor capture the diffusion of armed conflict, and hence do not adequately account for its dependence across both time and space. To address this, we introduce a regression approach that simultaneously captures both spatial and temporal dimension of the diffusion of armed conflict through non-parametric smoothing, while all its effects and parameters remain fully interpretable. Using fine-grained conflict data on Africa, we observe that diffusion exhibits long-lasting and far-reaching dependencies that decay exponentially in both space and time, thus highlighting the importance of controlling for these effects. We illustrate the flexibility of our method for studying conflict diffusion, by investigating the role of population in the transmission of conflict. We find that conflict typically breaks out in densely populated areas, and from there diffuses, specifically to lower population areas.