For a partition $λ\vdash n$, we let $\operatorname{pd}(λ)$, the parity difference of $λ$, be the number of odd parts of $λ$ minus the number of even parts of $λ$. We prove for $c_0\in\mathbb{R}$ an asymptotic expansion for the number of partitions of $n$ into distinct parts with normalised parity difference $n^{- 1/4}\operatorname{pd}(λ)$ greater than $c_0$ as $n\to \infty$. As a corollary, we find the distribution of the parity differences and parity biases for partitions of $n$ into distinct parts. We also establish analogous results for generalised parity differences modulo $N$.