用扩散模型的生成路径对齐构建置信区间,无需概率计算。
TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Models

- 通过扩散/流匹配模型的去噪误差衡量输出与生成路径对齐程度
- 在真实和合成数据上实现有效覆盖率,适应多模态分布
- 适合需要无假设置信区间的复杂生成任务
多维输出的可靠且信息丰富的置信预测区域构建仍是基础挑战。虽然置信预测提供有限样本、分布无关的覆盖保证,但其实际性能高度依赖非符合性得分的选择。现有方法常依赖严格几何假设或需显式似然计算与可逆变换,在复杂生成场景中应用受限。本文提出TRACE(Transport Alignment Conformal Estimation),通过扩散与流匹配模型中的传输对齐定义非符合性得分。不进行似然评估,而是沿随机传输轨迹平均去噪或速度匹配误差,衡量候选输出与学习到的生成动态的对齐程度。所得得分是标量,可通过分隔置信预测校准,在交换性条件下实现有效的边际覆盖。我们进一步分析了所提得分的统计性质及其对计算预算的敏感性。在合成与真实数据集上的实验表明,该方法实现了有效覆盖,并能自然适应多模态与非凸条件分布。
原文摘要 · Abstract (English)
Constructing valid and informative conformal prediction regions for multi-dimensional outputs remains a fundamental challenge. While conformal prediction provides finite-sample, distribution-free coverage guarantees, its practical performance critically depends on the choice of nonconformity score. Existing approaches often rely on restrictive geometric assumptions or require explicit likelihood evaluation and invertible transformations, limiting their applicability in complex generative settings. In this work, we introduce TRACE (TRansport Alignment Conformal Estimation), a conformal prediction framework that defines nonconformity through transport alignment in diffusion and flow matching models. Rather than evaluating likelihoods, we measure how well a candidate output aligns with the learned generative dynamics by averaging denoising or velocity-matching errors along stochastic transport trajectories. The resulting transport-based scores are scalar-valued and can be calibrated using split conformal prediction, yielding valid marginal coverage under exchangeability. We further analyze the statistical properties of the proposed scores and their sensitivity to computational budget. Experiments on synthetic and real datasets demonstrate valid coverage and show that the resulting regions adapt naturally to multimodal and non-convex conditional distributions.
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