Temporal analysis of synthetic aperture radar (SAR) time series is a basic and significant issue in the remote sensing field. Change detection as well as other interpretation tasks of SAR images always involves non-linear/non-convex problems. Complex (non-linear) change criteria or models have thus been proposed for SAR images, instead of direct difference (e.g., change vector analysis) with/without linear transform (e.g., Principal Component Analysis, Slow Feature Analysis) used in optical image change detection. In this paper, inspired by the powerful deep learning techniques, we present a deep autoencoder (AE) based non-linear subspace representation for unsupervised change detection with multi-temporal SAR images. The proposed architecture is built upon an autoencoder-like (AE-like) network, which non-linearly maps the input SAR data into a latent space. Unlike normal AE networks, a self-expressive layer performing like principal component analysis (PCA) is added between the encoder and the decoder, which further transforms the mapped SAR data to mutually orthogonal subspaces. To make the proposed architecture more efficient at change detection tasks, the parameters are trained to minimize the representation difference of unchanged pixels in the deep subspace. Thus, the proposed architecture is namely the Differentially Deep Subspace Representation (DDSR) network for multi-temporal SAR images change detection. Experimental results on real datasets validate the effectiveness and superiority of the proposed architecture.For change detection using remotely sensed optical images, the most widely used criterion is difference operator [1] (for single channel images) or change vector analysis [6-8] (for multi-band/spectral images). Due to the temporal spectral variance caused by different atmospheric conditions, illumination and sensor calibration, image transformation has been widely used to yield robust change detection criteria. The core idea of the image transformation is to transform the multi-band/spectral image into a specific feature space, in which the unchanged temporal pixel pairs have similar representations while the changed ones differ from each other. Principal component analysis (PCA) [9][10][11] is one of the state-of-the-art operators for modeling temporal spectral difference of unchanged pixels. Beyond PCA, Kauth-Thomas transformation [12], Gram-Schmidt orthonormalization process [13,14], multivariate alteration detection [15,16] and slow feature analysis [17,18] theories have been used for optical image change detection. However, these algorithms are mainly designed for optical images and usually fail to deal with SAR images with speckle.Given SAR images, we may meet a more complex situation in which the multi-temporal images are in different feature spaces and changed/unchanged pixels are linearly non-sparable, due to the coherent imaging mechanism. Two main approaches have been developed in the literature: coherence change detection and incoherent change detection. The former uses the phase inf...