Compressed sensing (CS) techniques have enabled efficient acquisition and recovery of sparse high-dimensional data via succinct low-dimensional projections, which usually consist of an encoder and a decoder. Unlike conventional CS techniques with the encoding-decoding architecture, the uncertainty autoencoder (UAE) can sample from the learned input data distribution without an explicit likelihood function, hence avoids potential uninformative latent representations. However, existing works on UAE mainly focus on the encoders and maximize the lower bound of the mutual information between input and measurements, rather than the decoders, which brings the shortcoming that the two may not cope well. In this letter, we propose a novel training scheme for UAE that blurs the measurements to learn the encoder and decoder simultaneously. Experimental results show that the proposed method improves the reconstruction performances when applied to UAE.