Although Large Language Models (LLMs) have made remarkable progress, current preference optimization methods still struggle to align directional consistency while preserving reasoning diversity. To address this limitation, we propose Directional-Groupwise Preference Optimization (DGPO), a lightweight framework that aggregates supervision signals at the group level and explicitly models direction-aware alignment through multi-candidate comparisons. DGPO organizes forward and reverse question-answer instances into structured sets and optimizes a margin-based likelihood objective that separates coherent reasoning paths from inconsistent alternatives. This groupwise formulation captures richer relative information than pairwise objectives and reinforces consistency across diverse reasoning pathways. Empirical results show that our constructed reverse data yields a 3.2% average improvement across five benchmarks, while DGPO further delivers consistent gains across multiple datasets and model families, achieving average accuracy improvements of up to 3.6%. Our code and data are available at https://github.com/Demi-deng2/DGPO.

Evaluating the factuality of long-form generations from Large Language Models (LLMs) remains challenging due to accuracy issues and costly human assessment. Prior evaluation pipelines attempt this by decomposing text into claims, searching for evidence, and verifying claims, but suffer from critical drawbacks: (1) inefficiency due to complex pipeline components unsuitable for long LLM outputs, and (2) ineffectiveness stemming from inaccurate claim sets and insufficient evidence collection of one-line SERP snippets. To address these limitations, we adapt the existing decompose-then-verify evaluation framework and propose FaStFact, a fast and strong evaluation pipeline that achieves the highest alignment with human evaluation and efficiency among existing baselines. FaStFact first employs chunk-level claim extraction integrated with confidence-based pre-verification, significantly reducing the cost of web searching and inference calling while ensuring reliability. For searching and verification, it gathers document-level evidence from crawled website pages for retrieval during verification, addressing the evidence insufficiency problem in previous pipelines. Extensive experiments based on an aggregated and manually annotated benchmark demonstrate the reliability of FaStFact in both efficiently and effectively evaluating the factuality of long-form LLM generations. We submit the paper with code and benchmark, and will make them publicly available to facilitate research.