Significance The generation and serial interval distributions are key, but different, quantities in outbreak analyses. Recent studies suggest that the two distributions give different estimates of the reproduction number R as inferred from the observed growth rate r . Here, we show that estimating R based on r and the serial interval distribution, when defined from the correct reference cohort, gives the same estimate as using r and the generation interval distribution. We apply our framework to COVID-19 serial interval data from China, outside Hubei province (January 21 to February 8, 2020), revealing systematic biases in prior inference methods. Our study provides the theoretical basis for practical changes to the principled use of serial interval distributions in estimating R during epidemics.