Modern face recognition (FR) models excel in constrained scenarios, but often suffer from decreased performance when deployed in unconstrained (real-world) environments due to uncertainties surrounding the quality of the captured facial data. Face image quality assessment (FIQA) techniques aim to mitigate these performance degradations by providing FR models with sample-quality predictions that can be used to reject low-quality samples and reduce false match errors. However, despite steady improvements, ensuring reliable quality estimates across facial images with diverse characteristics remains challenging. In this paper, we present a powerful new FIQA approach, named DifFIQA, which relies on denoising diffusion probabilistic models (DDPM) and ensures highly competitive results. The main idea behind the approach is to utilize the forward and backward processes of DDPMs to perturb facial images and quantify the impact of these perturbations on the corresponding image embeddings for quality prediction. Because the diffusion-based perturbations are computationally expensive, we also distill the knowledge encoded in DifFIQA into a regression-based quality predictor, called DifFIQA(R), that balances performance and execution time. We evaluate both models in comprehensive experiments on 7 datasets, with 4 target FR models and against 10 state-of-the-art FIQA techniques with highly encouraging results. The source code will be made publicly available.