Hyperspectral unmixing is a fundamental task in remote sensing that aims to decompose mixed spectral pixels into their constituent materials and estimate their respective abundances. Traditional methods often face limitations due to nonlinear mixing effects and the lack of pure pixels. This paper proposes a deep learning-based comparative framework that integrates modified versions of the Minimum Simplex Convolutional Network (MiSiCNet) and Unsupervised Deep Image Prior (UnDIP), referred to as Blind MiSiCNet and Supervised UnDIP, respectively, to achieve robust unmixing and abundance estimation in real-world scenarios. The proposed Blind MiSiCNet removes downsampling and upsampling layers and leverages spatial and geometric priors through convolutional layers with a minimum simplex volume constraint, producing reliable initial abundance maps even in the absence of pure pixels. The Supervised UnDIP variant further refines these estimates using the implicit regularization of convolutional neural networks, incorporating known endmembers to generate noise-free and spatially coherent abundance maps. Experimental results on the real-world Jasper Ridge dataset demonstrate that the proposed supervised and blind unmixing methods, evaluated comparatively, significantly outperform existing approaches regarding Spectral Angle Distance (SAD) and Root Mean Square Error (RMSE). The results also highlight improved noise robustness and better preservation of spatial structures.