Diffusion probabilistic models (DPMs) have become the state-of-the-art in high-quality image generation. However, DPMs have an arbitrary noisy latent space with no interpretable or controllable semantics. Although there has been significant research effort to improve image sample quality, there is little work on representation-controlled generation using diffusion models. Specifically, causal modeling and controllable counterfactual generation using DPMs is an underexplored area. In this work, we propose CausalDiffAE, a diffusion-based causal representation learning framework to enable counterfactual generation according to a specified causal model. Our key idea is to use an encoder to extract high-level semantically meaningful causal variables from high-dimensional data and model stochastic variation using reverse diffusion. We propose a causal encoding mechanism that maps high-dimensional data to causally related latent factors and parameterize the causal mechanisms among latent factors using neural networks. To enforce the disentanglement of causal variables, we formulate a variational objective and leverage auxiliary label information in a prior to regularize the latent space. We propose a DDIM-based counterfactual generation procedure subject to do-interventions. Finally, to address the limited label supervision scenario, we also study the application of CausalDiffAE when a part of the training data is unlabeled, which also enables granular control over the strength of interventions in generating counterfactuals during inference. We empirically show that CausalDiffAE learns a disentangled latent space and is capable of generating high-quality counterfactual images.

翻译：扩散概率模型已成为高质量图像生成的最新技术。然而，扩散概率模型具有任意的含噪潜空间，缺乏可解释或可控制的语义特性。尽管已有大量研究致力于提升图像样本质量，但基于扩散模型实现表征控制生成的相关工作仍十分有限。特别是，利用扩散概率模型进行因果建模与可控反事实生成仍是亟待探索的研究领域。本文提出CausalDiffAE——一种基于扩散的因果表征学习框架，旨在根据指定因果模型实现反事实生成。我们的核心思想是：通过编码器从高维数据中提取具有高级语义意义的因果变量，并利用反向扩散过程对随机变化进行建模。我们提出因果编码机制，将高维数据映射至具有因果关联的潜在因子，并通过神经网络参数化潜在因子间的因果机制。为强制因果变量解耦，我们构建变分目标函数，并利用先验中的辅助标签信息规范潜空间。我们提出基于DDIM的干预操作反事实生成流程。最后，针对有限标签监督场景，我们进一步研究了部分训练数据无标签时CausalDiffAE的应用，该方法可在推理阶段实现干预强度的精细调控以生成反事实结果。实验表明，CausalDiffAE能够学习解耦的潜空间，并生成高质量的反事实图像。