The exceptional performance of diffusion models establishes them as high-value intellectual property but exposes them to unauthorized replication. Existing protection methods either modify the model to embed watermarks, which impairs performance, or extract model fingerprints by manipulating the denoising process, rendering them incompatible with black-box APIs. In this paper, we propose TrajPrint, a completely lossless and training-free framework that verifies model copyright by extracting unique manifold fingerprints formed during deterministic generation. Specifically, we first utilize a watermarked image as an anchor and exactly trace the path back to its trajectory origin, effectively locking the model fingerprint mapped by this path. Subsequently, we implement a joint optimization strategy that employs dual-end anchoring to synthesize a specific fingerprint noise, which strictly adheres to the target manifold for robust watermark recovery. As input, it enables the protected target model to recover the watermarked image, while failing on non-target models. Finally, we achieved verification via atomic inference and statistical hypothesis testing. Extensive experiments demonstrate that TrajPrint achieves lossless verification in black-box API scenarios with superior robustness against model modifications.

翻译：扩散模型的卓越性能使其成为高价值的知识产权，但也使其面临未经授权复制的风险。现有的保护方法要么通过修改模型嵌入水印（这会损害模型性能），要么通过操纵去噪过程提取模型指纹（导致其无法与黑盒API兼容）。本文提出TrajPrint，一个完全无损且无需训练的框架，通过提取确定性生成过程中形成的独特流形指纹来验证模型版权。具体而言，我们首先利用带水印图像作为锚点，精确追溯其轨迹起源路径，从而有效锁定由该路径映射的模型指纹。随后，我们采用联合优化策略，通过双端锚定合成特定的指纹噪声，该噪声严格遵循目标流形以实现鲁棒的水印恢复。作为输入，该噪声能使受保护的目标模型恢复带水印图像，而在非目标模型上则无法实现。最后，我们通过原子推理与统计假设检验完成验证。大量实验表明，TrajPrint在黑盒API场景下实现了无损验证，并对模型修改具有卓越的鲁棒性。