While the current trend in the generative field is scaling up towards larger models and more training data for generalized domain representations, we go the opposite direction in this work by synthesizing unseen domain images without additional training. We do so via latent sampling and geometric optimization using pre-trained and frozen Denoising Diffusion Probabilistic Models (DDPMs) on single-domain datasets. Our key observation is that DDPMs pre-trained even just on single-domain images are already equipped with sufficient representation abilities to reconstruct arbitrary images from the inverted latent encoding following bi-directional deterministic diffusion and denoising trajectories. This motivates us to investigate the statistical and geometric behaviors of the Out-Of-Distribution (OOD) samples from unseen image domains in the latent spaces along the denoising chain. Notably, we theoretically and empirically show that the inverted OOD samples also establish Gaussians that are distinguishable from the original In-Domain (ID) samples in the intermediate latent spaces, which allows us to sample from them directly. Geometrical domain-specific and model-dependent information of the unseen subspace (e.g., sample-wise distance and angles) is used to further optimize the sampled OOD latent encodings from the estimated Gaussian prior. We conduct extensive analysis and experiments using pre-trained diffusion models (DDPM, iDDPM) on different datasets (AFHQ, CelebA-HQ, LSUN-Church, and LSUN-Bedroom), proving the effectiveness of this novel perspective to explore and re-think the diffusion models' data synthesis generalization ability.

翻译：尽管当前生成领域的主流趋势是扩大模型规模与训练数据量以实现通用域表征，我们却反其道而行之，提出无需额外训练即可合成未见域图像的方法。该方法基于单域数据集上预训练且冻结的去噪扩散概率模型（DDPM），通过潜在空间采样与几何优化实现。我们的关键发现是：即便仅在单域图像上预训练的DDPM，其表征能力已足以依据双向确定性扩散与去噪轨迹，从逆向潜在编码中重构任意图像。这促使我们沿去噪链探究未见图像域中分布外样本（OOD）在潜在空间内的统计与几何行为。值得关注的是，我们从理论与实验两方面证明：逆向OOD样本在中间潜在空间形成的分布同样可构建高斯分布，且该分布与原始域内样本（ID）可区分，从而允许直接从中采样。通过利用未见子空间几何化的域特定与模型依赖信息（如样本间距离与角度），可进一步优化基于估计高斯先验的OOD潜在编码采样结果。我们在不同数据集（AFHQ、CelebA-HQ、LSUN-Church与LSUN-Bedroom）上使用预训练扩散模型（DDPM、iDDPM）开展广泛分析与实验，验证了这一探索扩散模型数据合成泛化能力新视角的有效性。