Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the standard Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories, and demonstrate how the framework may be adopted for learning bridges between two distributions. The results underscores NFDM's versatility and its potential for a wide range of applications.

翻译：传统的扩散模型通常依赖于固定的正向过程，该过程隐式地定义了潜变量的复杂边缘分布。这往往会使逆向过程在学习生成轨迹时任务复杂化，并导致扩散模型的推理成本高昂。为应对这些局限，我们提出了神经流扩散模型（NFDM），这是一种新颖的框架，通过支持超越标准高斯分布的更广泛正向过程来增强扩散模型。我们还提出了一种用于学习正向过程的新颖参数化技术。我们的框架提供了一个端到端、无需模拟的优化目标，有效地最小化负对数似然的变分上界。实验结果表明NFDM具有强大的性能，其最先进的似然估计能力即为明证。此外，我们研究了NFDM学习具有特定特性（如确定性直线轨迹）的生成动力学的能力，并展示了该框架如何可用于学习两个分布之间的桥接。这些结果突显了NFDM的通用性及其在广泛应用中的潜力。