Quantitative MRI (qMRI) offers significant advantages over weighted images by providing objective parameters related to tissue properties. Deep learning-based methods have demonstrated effectiveness in estimating quantitative maps from series of weighted images. In this study, we present qMRI Diffuser, a novel approach to qMRI utilising deep generative models. Specifically, we implemented denoising diffusion probabilistic models (DDPM) for T1 quantification in the brain, framing the estimation of quantitative maps as a conditional generation task. The proposed method is compared with the residual neural network (ResNet) and the recurrent inference machine (RIM) on both phantom and in vivo data. The results indicate that our method achieves improved accuracy and precision in parameter estimation, along with superior visual performance. Moreover, our method inherently incorporates stochasticity, enabling straightforward quantification of uncertainty. Hence, the proposed method holds significant promise for quantitative MR mapping.@en