用量子算法加速扩散模型生成，降低高维数据训练成本。
Towards efficient quantum algorithms for diffusion probabilistic models
- 采用量子微分方程求解器实现扩散模型，结合量子线性系统求解与哈密顿模拟。
- 提出DPM-solver-k和UniPC两种方法，分别用高阶导数与有限差分逼近噪声预测函数。
- 为大规模机器学习模型的量子化应用提供直接路径，适合量子计算与生成模型研究者。
扩散概率模型（DPM）是生成高质量图像和音频等任务的重要模型，但其在高分辨率图像或音频等大规模高维数据上的训练存在显著的计算、能耗和硬件开销。本文引入高效的量子算法，通过多种量子常微分方程求解器实现DPM的构建。算法利用前沿量子线性系统求解器（QLSS）和哈密顿量线性组合（LCHS），展现量子Carleman线性化在多样化数学结构中的潜力。具体提出两种方法：DPM-solver-k利用精确的k阶导数计算ε_θ(x_λ,λ)的多项式逼近；UniPC则通过在不同点(x_{s_m}, λ_{s_m})上对ε_θ进行有限差分，近似高阶导数。本工作是量子算法在大规模机器学习模型中最具直接性和实用性的应用之一，有望推动量子计算的实际价值验证。
原文摘要 · Abstract (English)
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as high-resolution images or audio incurs significant computational, energy, and hardware costs. In this work, we introduce efficient quantum algorithms for implementing DPMs through various quantum ODE solvers. These algorithms highlight the potential of quantum Carleman linearization for diverse mathematical structures, leveraging state-of-the-art quantum linear system solvers (QLSS) or linear combination of Hamiltonian simulations (LCHS). Specifically, we focus on two approaches: DPM-solver-$k$ which employs exact $k$-th order derivatives to compute a polynomial approximation of $ε_θ(x_λ,λ)$; and UniPC which uses finite difference of $ε_θ(x_λ,λ)$ at different points $(x_{s_m}, λ_{s_m})$ to approximate higher-order derivatives. As such, this work represents one of the most direct and pragmatic applications of quantum algorithms to large-scale machine learning models, presumably taking substantial steps towards demonstrating the practical utility of quantum computing.
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