We propose SketchPlan, a diffusion-based planner that interprets 2D hand-drawn sketches over depth images to generate 3D flight paths for drone navigation. SketchPlan comprises two components: a SketchAdapter that learns to map the human sketches to projected 2D paths, and DiffPath, a diffusion model that infers 3D trajectories from 2D projections and a first person view depth image. Our model achieves zero-shot sim-to-real transfer, generating accurate and safe flight paths in previously unseen real-world environments. To train the model, we build a synthetic dataset of 32k flight paths using a diverse set of photorealistic 3D Gaussian Splatting scenes. We automatically label the data by computing 2D projections of the 3D flight paths onto the camera plane, and use this to train the DiffPath diffusion model. However, since real human 2D sketches differ significantly from ideal 2D projections, we additionally label 872 of the 3D flight paths with real human sketches and use this to train the SketchAdapter to infer the 2D projection from the human sketch. We demonstrate SketchPlan's effectiveness in both simulated and real-world experiments, and show through ablations that training on a mix of human labeled and auto-labeled data together with a modular design significantly boosts its capabilities to correctly interpret human intent and infer 3D paths. In real-world drone tests, SketchPlan achieved 100\% success in low/medium clutter and 40\% in unseen high-clutter environments, outperforming key ablations by 20-60\% in task completion.