In diffusion models, deviations from a straight generative flow are a common issue, resulting in semantic inconsistencies and suboptimal generations. To address this challenge, we introduce `Non-Cross Diffusion', an innovative approach in generative modeling for learning ordinary differential equation (ODE) models. Our methodology strategically incorporates an ascending dimension of input to effectively connect points sampled from two distributions with uncrossed paths. This design is pivotal in ensuring enhanced semantic consistency throughout the inference process, which is especially critical for applications reliant on consistent generative flows, including various distillation methods and deterministic sampling, which are fundamental in image editing and interpolation tasks. Our empirical results demonstrate the effectiveness of Non-Cross Diffusion, showing a substantial reduction in semantic inconsistencies at different inference steps and a notable enhancement in the overall performance of diffusion models.
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