Monocular depth estimation has seen significant advances through discriminative approaches, yet their performance remains constrained by the limitations of training datasets. While generative approaches have addressed this challenge by leveraging priors from internet-scale datasets, with recent studies showing state-of-the-art results using fine-tuned text-to-image diffusion models, there is still room for improvement. Notably, autoregressive generative approaches, particularly Visual AutoRegressive modeling, have demonstrated superior results compared to diffusion models in conditioned image synthesis, while offering faster inference times. In this work, we apply Visual Autoregressive Transformer (VAR) to the monocular depth estimation problem. However, the conventional GPT-2-style training procedure (teacher forcing) inherited by VAR yields suboptimal results for depth estimation. To address this limitation, we introduce DepthART - a novel training method formulated as a Depth Autoregressive Refinement Task. Unlike traditional VAR training with static inputs and targets, our method implements a dynamic target formulation based on model outputs, enabling self-refinement. By utilizing the model's own predictions as inputs instead of ground truth token maps during training, we frame the objective as residual minimization, effectively reducing the discrepancy between training and inference procedures. Our experimental results demonstrate that the proposed training approach significantly enhances the performance of VAR in depth estimation tasks. When trained on Hypersim dataset using our approach, the model achieves superior results across multiple unseen benchmarks compared to existing generative and discriminative baselines.