Normalizing Flows (NFs) learn invertible mappings between the data and a Gaussian distribution. Prior works usually suffer from two limitations. First, they add random noise to training samples or VAE latents as data augmentation, introducing complex pipelines including extra noising and denoising steps. Second, they use a pretrained and frozen VAE encoder, resulting in suboptimal reconstruction and generation quality. In this paper, we find that the two issues can be solved in a very simple way: just fixing the variance (which would otherwise be predicted by the VAE encoder) to a constant (e.g., 0.5). On the one hand, this method allows the encoder to output a broader distribution of tokens and the decoder to learn to reconstruct clean images from the augmented token distribution, avoiding additional noise or denoising design. On the other hand, fixed variance simplifies the VAE evidence lower bound, making it stable to train an NF with a VAE jointly. On the ImageNet $256 \times 256$ generation task, our model SimFlow obtains a gFID score of 2.15, outperforming the state-of-the-art method STARFlow (gFID 2.40). Moreover, SimFlow can be seamlessly integrated with the end-to-end representation alignment (REPA-E) method and achieves an improved gFID of 1.91, setting a new state of the art among NFs.

翻译：归一化流通过可逆映射将数据分布与高斯分布相互转换。现有方法通常存在两个局限：其一，它们在训练样本或变分自编码器潜在空间中添加随机噪声作为数据增强，引入了包含额外加噪与去噪步骤的复杂流程；其二，它们使用预训练且冻结的VAE编码器，导致重建与生成质量欠佳。本文发现这两个问题可通过一种极简方案解决：仅需将VAE编码器原本预测的方差固定为常数（例如0.5）。该方法一方面使编码器能输出更广泛的标记分布，同时让解码器学会从增强后的标记分布中重建清晰图像，从而无需额外的噪声设计或去噪模块；另一方面，固定方差简化了VAE证据下界，使得联合训练VAE与NF的过程更为稳定。在ImageNet $256 \\times 256$生成任务中，我们的SimFlow模型取得了2.15的gFID分数，优于当前最优方法STARFlow（gFID 2.40）。此外，SimFlow可与端到端表示对齐方法REPA-E无缝集成，获得1.91的gFID分数，在NF类方法中创造了新的性能纪录。