Abstract: Transformer models can face practical limitations due to their high computational requirements. At the same time, they exhibit high activation sparsity, which can be leveraged to reduce the inference cost by converting parts of the network into equivalent Mixture-of-Experts~(MoE) layers. Despite the crucial role played by activation sparsity, its impact on this process remains unexplored. In particular, we show that the efficiency of the conversion can be significantly enhanced by a proper regularization of the activation sparsity of the base model. Moreover, motivated by the high variance of the number of activated neurons for different inputs, we introduce a more effective dynamic-$k$ expert selection rule that adjusts the number of executed experts on a per-token basis. The proposed method, Dense to Dynamic-$k$ Mixture-of-Experts (D2DMoE), outperforms existing approaches on common NLP and vision tasks, allowing us to save up to 60\% of inference cost without significantly affecting model performance.