Blind face restoration (BFR) is a challenging problem because of the uncertainty of the degradation patterns. This paper proposes a Restoration with Memorized Modulation (RMM) framework for universal BFR in diverse degraded scenes and heterogeneous domains. We apply random noise as well as unsupervised wavelet memory to adaptively modulate the face-enhancement generator, considering attentional denormalization in both layer and instance levels. Specifically, in the training stage, the low-level spatial feature embedding, the wavelet memory embedding obtained by wavelet transformation of the high-resolution image, as well as the disentangled high-level noise embeddings are integrated, with the guidance of attentional maps generated from layer normalization, instance normalization and the original feature map. These three embeddings are respectively associated with the spatial content, high-frequency texture details, and a learnable universal prior against other blind image degradation patterns. We store the spatial feature of the low-resolution image and the corresponding wavelet style code as key and value in the memory unit, respectively. In the test stage, the wavelet memory value whose corresponding spatial key is the most matching with that of the inferred image is retrieved to modulate the generator. Moreover, the universal prior learned from the random noise has been memorized by training the modulation network. Experimental results show the superiority of the proposed method compared with the state-of-the-art models, and a good generalization in the wild.