Creative sketching or doodling is an expressive activity, where imaginative and previously unseen depictions of everyday visual objects are drawn. Creative sketch image generation is a challenging vision problem, where the task is to generate diverse, yet realistic creative sketches possessing the unseen composition of the visual-world objects. Here, we propose a novel coarse-to-fine two-stage framework, DoodleFormer, that decomposes the creative sketch generation problem into the creation of coarse sketch composition followed by the incorporation of fine-details in the sketch. We introduce graph-aware transformer encoders that effectively capture global dynamic as well as local static structural relations among different body parts. To ensure diversity of the generated creative sketches, we introduce a probabilistic coarse sketch decoder that explicitly models the variations of each sketch body part to be drawn. Experiments are performed on two creative sketch datasets: Creative Birds and Creative Creatures. Our qualitative, quantitative and human-based evaluations show that DoodleFormer outperforms the state-of-the-art on both datasets, yielding realistic and diverse creative sketches. On Creative Creatures, DoodleFormer achieves an absolute gain of 25 in Frèchet inception distance (FID) over state-of-the-art. We also demonstrate the effectiveness of DoodleFormer for related applications of text to creative sketch generation, sketch completion and house layout generation. Code is available at: https://github.com/ankanbhunia/doodleformer. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.