打破扩散模型默认正态噪声假设，用非正态增量提升生成灵活性。
Non-Normal Diffusion Models
- 引入非正态分布的扩散步长Δx_k，突破传统正态假设限制。
- 在标准图像数据集上实现更好的密度估计与生成效果，不同分布产生不同风格样本。
- 适合对生成多样性与可控性有要求的研究者与应用开发者。
扩散模型通过逐步反转将数据变为噪声的过程来生成样本。我们发现当步长趋近于零时，反向过程对增量分布具有不变性。这揭示了扩散模型设计中一个此前未被关注的参数：扩散步长Δx_k := x_k - x_{k+1}的分布。当前多数扩散模型默认该分布为正态。通过解除这一假设，我们扩展了扩散模型的设计框架，建立了更灵活的损失函数选择空间。我们在标准图像数据集上验证了这些模型在密度估计和生成建模任务中的有效性，并表明Δx_k的不同分布会带来定性不同的生成结果。
原文摘要 · Abstract (English)
Diffusion models generate samples by incrementally reversing a process that turns data into noise. We show that when the step size goes to zero, the reversed process is invariant to the distribution of these increments. This reveals a previously unconsidered parameter in the design of diffusion models: the distribution of the diffusion step $Δx_k := x_{k} - x_{k + 1}$. This parameter is implicitly set by default to be normally distributed in most diffusion models. By lifting this assumption, we generalize the framework for designing diffusion models and establish an expanded class of diffusion processes with greater flexibility in the choice of loss function used during training. We demonstrate the effectiveness of these models on density estimation and generative modeling tasks on standard image datasets, and show that different choices of the distribution of $Δx_k$ result in qualitatively different generated samples.
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