Is Imagination Derived from Hallucination? A Cross-Taxonomy Evaluation of Imagination and Hallucination in Large Language Models

Imagination performs as a high-level function of large language models (LLMs) which determines the potential of how an LLM creates unseen or creative content. While existing works have built a rich family of creativity benchmarks for this ability, they only measure how far an output departs from common answers and never check whether the departure is licensed by the prompt. Moreover, hallucination, the closest neighbor of imagination, is always measured in a separate pipeline on different generations, so the influential claim that imagination and hallucination stem from the same generative mechanism has never been directly testable. In this paper, we propose Whiteboard, the first LLM imagination evaluation benchmark. Its design follows the authoritative cognitive instruments developed to measure human imagination: seven mechanism-grounded imagination subtypes are adapted from classic paradigms, then crossed with ten support-boundary hallucination subtypes and scored jointly on the same generation. Different from previous creativity or hallucination benchmarks, Whiteboard gates every imagination score with an explicit support check and computes both axes deterministically through an auditable atom matrix, with no LLM judge on the primary path. The full Whiteboard item bank contains 1,660 prompts; on its shared 80-item anchor set, we evaluate 79 state-of-the-art LLMs and validate the instrument against 13,280 human judgments. Additionally, we further explore whether imagination derives from the same generative tendency as hallucination and what key factors shape it. Our analysis indicates a counterintuitive correlation between hallucination and imagination: Most of the subtype couplings are negative, every one of the anchor items reproduces the negative coupling on its own.