Large language models (LLMs) frequently hallucinate when confronted with queries they cannot answer reliably. The root causes are multifaceted, including entity rarity, semantic ambiguity, temporal invalidity, false presuppositions, and other forms of epistemic uncertainty. Existing abstention mechanisms overwhelmingly rely on binary probes trained with manually curated “unanswerable” labels or calibrated confidence scores, both of which presuppose access to negative examples that are expensive to collect and fundamentally incomplete in coverage. We propose FLOW-ABSTAIN, an unsupervised framework that reframes query-aware abstention as density estimation in the model’s own latent space. Our method operates in three stages: (1) extracting intermediate hidden-state representations from a curated set of confidently answerable queries, (2) applying PCA-based dimensionality reduction to obtain a compact manifold, and (3) fitting a Masked Autoregressive Flow (MAF) to the resulting representations, yielding an exact, tractable log-likelihood for arbitrary new inputs. At inference time, queries whose latent projections receive low log-likelihood under the learned density are flagged for abstention—without requiring any negative or out-of-distribution training samples. Experiments across three instruction-tuned LLMs (Qwen-3-8B, Qwen-3-14B, Llama-3-8B-Instruct) and five diverse evaluation benchmarks demonstrate that FLOW-ABSTAIN achieves highly competitive abstention performance among methods with practical inference cost while providing a continuous, interpretable likelihood signal that naturally stratifies query difficulty along cognitive dimensions of unanswerability.