Understanding both the population or subclonal structure and evolutionary forces that drive tumour evolution has important clinical implications for patients. However, deconvoluting subclonal structure and performing evolutionary parameter inference have largely been treated as two independent or step-wise tasks. Here, we show that combining stochastic simulations with hybrid deep generative models enables joint inference of subclonal structure and evolutionary parameter estimates. Ultimately, by jointly learning these two tasks, we show that our proposed approach leads to improve performance across a multitude of cancer evolution tasks including, but not limited to, detecting subclones, quantifying subclone frequency, and estimating mutation rate. As an additional benefit, we also show that hybrid deep generative models also provide substantial reductions in inference time relative to existing methods.