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We present the Cross-stitched Multi-task Unified Dual Recursive Network (CMUDRN) model targeting the task of unified deraining and desnowing in a multi-task learning setting. This unified model borrows from the basic Dual Recursive Network (DRN) architecture developed by Cai et al. The proposed model makes use of cross-stitch units that enable multi-task learning across two separate DRN models, each tasked for single image deraining and desnowing, respectively. By fixing cross-stitch units at several layers of basic task-specific DRN networks, we perform multi-task learning over the two separate DRN models. To enable blind image restoration, on top of these structures we employ a simple neural fusion scheme which merges the output of each DRN. The separate task-specific DRN models and the fusion scheme are simultaneously trained by enforcing local and global supervision. Local supervision is applied on the two DRN submodules, and global supervision is applied on the data fusion submodule of the proposed model. Consequently, we both enable feature sharing across task-specific DRN models and control the image restoration behavior of the DRN submodules. An ablation study shows the strength of the hypothesized CMUDRN model, and experiments indicate that its performance is comparable or better than baseline DRN models on the single image deraining and desnowing tasks. Moreover, CMUDRN enables blind image restoration for the two underlying image restoration tasks, by unifying task-specific image restoration pipelines via a naive parametric fusion scheme. The CMUDRN implementation is available at https://github.com/VCL3D/CMUDRN.