Editable diagram generation from natural language requires structural correctness and visual readability. Text-to-image models produce rasters with no editable objects. LLM code-generation approaches yield editable output but face three challenges: unreliable geometry from token-by-token coordinate emission, shallow verification that checks code rather than the rendered image, and dependence on task-specific fine-tuning. We present VISTA, a training-free pipeline that assigns each subproblem to the appropriate component: an LLM extracts semantic structure, a deterministic algorithm computes all geometry, and a VLM inspects the rendered diagram jointly with its source and issues localized repairs. We construct a 150-prompt benchmark from PNG-only references and evaluate against eight baselines including Codex, Claude Code, and a fine-tuned multi-agent system. VISTA achieves the highest readability across all pairwise comparisons. Code and data are available at https://github.com/nice-grp/Vista.