This paper studies the role of supply base diversification on the propagation of shocks through production networks. We identify exogenous shocks with the occurrence of natural disasters in the US between 1978 and 2017. We find that affected suppliers reduce customers' sales growth by ≈ 30%, on average. Notably, firms with intermediate input purchases spanning many suppliers, geographies, or producers within an industry attenuate shocks to their suppliers by ≈ 60-70%. We then show, causally, that diverse firms mitigate shocks by temporarily substituting towards unaffected suppliers producing similar inputs. We interpret our empirical findings using a general equilibrium model of production networks. We first establish that diverse firms exhibit gross substitutability across suppliers relative to non-diverse firms. We use the model to estimate the macroeconomic effect of supply base diversity, and find that aggregate volatility would have been ≈ 33% greater between 1978 and 2017 in the absence of input substitution by diversified firms in response to supply shocks.