A novel estimation method for distribution regressions in a network setting is proposed. It considers the effects of covariates on the entire outcome distribution rather than solely on the mean. I adopt a semiparametric approach by considering two-way unit-specific effects. Thus, I extend the standard distribution regression approach to a network setting by estimating multiple binary choice models with two-way fixed effects for different thresholds of the distribution. I employ a conditional maximum-likelihood approach that differences out the unit-specific effects, avoiding the incidental parameter problem. This method yields consistent point estimates that converge at a parametric rate and remain asymptotically unbiased in the tails of the outcome distribution, where the underlying network can be seen as sparse. Monte Carlo simulations validate these findings for single cut-off points and the overall outcome distribution. The empirical application focuses on gravity equations for bilateral trade, demonstrating the effectiveness of the proposed approach in cases where the outcome variable is bounded below at zero.