The widespread adoption of Low-Rank Adaptation (LoRA) for efficient fine-tuning of large language models has created demand for scalable parameter generation methods that can synthesize adaptation weights directly from task descriptions, avoiding costly task-specific training. We present LoRAGen, a structure-aware method for generating LoRA parameters from natural language descriptions. Through empirical analysis of LoRA libraries, we identify two key structural properties of LoRA parameter spaces: non-uniqueness of low-rank decomposition and heterogeneous weight distributions across network modules. These properties necessitate specialized parameter generation methods rather than general weight space learning approaches. LoRAGen employs a latent diffusion model with two innovations: weight-space supervision on full adaptation matrices to handle decomposition non-uniqueness, and a module-aware Mix-of-Experts decoder that adapts to module-specific weight distributions. Experiments show LoRAGen achieves 96.0\% performance relative to task-specific LoRAs on FLAN-T5-large and 72.7\% on Gemma-2-2B-Instruct for in-distribution tasks, while obtaining 40.2\% on zero-shot generation across unseen tasks—surpassing baselines by nearly 5\%. Our work establishes the first structure-aware approach to LoRA generation with insights into adaptation weight space geometry.