This survey provides a comprehensive guide to Multimodal Large Language Models (MLLMs) with a focus on vision–language tasks, including image captioning, visual question answering, cross-modal retrieval, visual grounding, multi-image reasoning, long-video understanding, and embodied AI. We examine architectures, training pipelines, and practical applications, covering visual encoders, language model backbones, connector modules, contrastive pre-training, instruction tuning, and preference alignment. We also foreground first-principles constraints—information bottlenecks, data-processing limits, and statistical co-occurrence bias—that shape architecture, robustness, and evaluation. This survey centers on vision–language systems and does not cover audio-only models or code-generation tools without visual inputs. Through task-level analysis and system-level case studies, we examine prominent MLLM implementations while addressing key challenges in scalability, memory, energy use, inference cost, robustness, and cross-modal learning. We present a unified taxonomy of the MLLM design space, a comparative overview of representative models and evaluation benchmarks, and a discussion of open problems. Concluding with ethical considerations and responsible AI development, this survey offers theoretical frameworks and practical insights for researchers, practitioners, and students working at the intersection of natural language processing and computer vision.

Traditional Chinese painting completion presents unique challenges where sparse ink distributions and intentional blank spaces serve aesthetic rather than functional purposes, contradicting assumptions in conventional inpainting methods. We propose Hierarchical Optimal Transport for Painting (HOT-Paint) that formulates completion as controlled texture redistribution in Wasserstein space. By interpreting texture synthesis through transport flow dynamics, we model brush stroke propagation using the static Kantorovich formulation while preserving characteristic sparsity through regularized transport plans.Our approach constructs multi-scale probability measures capturing artistic elements from fine strokes to global composition. The framework introduces adaptive cost functions integrating geometric distances, texture similarities via Gabor filters, and semantic relationships from pre-trained features. A modified Sinkhorn algorithm with soft-thresholding enforces sparsity constraints, while inter-scale consistency mechanisms ensure coherent information flow across resolutions. Experiments on CPDD and CelebA-HQ datasets demonstrate over 25.1% improvements in FID scores over state-of-the-art methods. Real-world restoration of authentic museum paintings validates practical utility. The proposed framework advances optimal transport theory for artistic image synthesis while addressing fundamental challenges in cultural heritage preservation.