用量子方法突破离散扩散模型的维度分解瓶颈,实现高效高精度生成。
Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning
- 提出量子联合分布学习框架,避免传统逐维计算导致的误差累积。
- 在高维数据上实现单步采样,相比迭代模型提速显著且更准确。
- 适合对生成质量要求高、需处理复杂高维结构的科研与工程场景。
离散扩散模型在生成复杂高质量离散数据方面取得显著进展,但为避免指数级计算开销,通常采用逐维概率计算。本文严格证明该方法在最坏情况下会导致KL散度随数据维度线性增长。为此,提出量子离散去噪扩散概率模型(QD3PM),通过在指数级希尔伯特空间中进行扩散与去噪,实现联合概率学习,为忠实捕捉真实联合分布提供理论路径。通过量子贝叶斯定理推导后验态,类比经典扩散模型中后验概率的关键作用,并学习联合分布,奠定量子增强扩散模型的理论基础。设计利用时间信息共享参数的量子电路,结合可学习的经典数据控制旋转以编码特征。借助联合分布学习,实现从纯噪声的单步采样,消除现有模型的迭代需求。仿真表明,该模型在建模复杂分布方面优于因子化方法,展现出更高精度。本文通过量子优势实现联合分布学习,建立生成模型的新理论范式。
原文摘要 · Abstract (English)
Discrete diffusion models represent a significant advance in generative modeling, demonstrating remarkable success in synthesizing complex, high-quality discrete data. However, to avoid exponential computational costs, they typically rely on calculating per-dimension transition probabilities when learning high-dimensional distributions. In this study, we rigorously prove that this approach leads to a worst-case linear scaling of Kullback-Leibler (KL) divergence with data dimension. To address this, we propose a Quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM), which enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces, offering a theoretical pathway to faithfully capture the true joint distribution. By deriving posterior states through quantum Bayes' theorem, similar to the crucial role of posterior probabilities in classical diffusion models, and by learning the joint probability, we establish a solid theoretical foundation for quantum-enhanced diffusion models. For denoising, we design a quantum circuit that utilizes temporal information for parameter sharing and incorporates learnable classical-data-controlled rotations for encoding. Exploiting joint distribution learning, our approach enables single-step sampling from pure noise, eliminating iterative requirements of existing models. Simulations demonstrate the proposed model's superior accuracy in modeling complex distributions compared to factorization methods. Hence, this paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
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