Diffusion models have achieved remarkable success in text-to-image synthesis, largely attributed to the use of classifier-free guidance (CFG), which enables high-quality, condition-aligned image generation. CFG combines the conditional score (e.g., text-conditioned) with the unconditional score to control the output. However, the unconditional score is in charge of estimating the transition between manifolds of adjacent timesteps from xtto xt−1, which may inadvertently interfere with the trajectory toward the specific condition. In this work, we introduce a novel approach that leverages a geometric perspective on the unconditional score to enhance CFG performance when conditional scores are available. Specifically, we propose a method that filters the singular vectors of both conditional and unconditional scores using singular value decomposition. This filtering process aligns the unconditional score with the conditional score, thereby refining the sampling trajectory to stay closer to the manifold. Our approach improves image quality with negligible additional computation. We provide deeper insights into the score function behavior in diffusion models and present a practical technique for achieving more accurate and contextually coherent image synthesis. project page

Rectified flow is a generative model that learns smooth transport mappings between two distributions through an ordinary differential equation (ODE). The model learns a straight ODE by reflow steps which iteratively update the supervisory flow. It allows for a relatively simple and efficient generation of high-quality images. However, rectified flow still faces several challenges. 1) The reflow process is slow because it requires a large number of generated pairs to model the target distribution. 2) It is well known that the use of suboptimal fake samples in reflow can lead to performance degradation of the learned flow model. This issue is further exacerbated by error accumulation across reflow steps and model collapse in denoising autoencoder models caused by self-consuming training. In this work, we go one step further and empirically demonstrate that the reflow process causes the learned model to drift away from the target distribution, which in turn leads to a growing discrepancy in reconstruction error between fake and real images. We reveal the drift problem and design a new reflow step, namely the conic reflow. It supervises the model by the inversions of real data points through the previously learned model and its interpolation with random initial points. Our conic reflow leads to multiple advantages. 1) It keeps the ODE paths toward real samples, evaluated by reconstruction. 2) We use only a small number of generated samples instead of large generated samples, 600K and 4M, respectively. 3) The learned model generates images with higher quality evaluated by FID, IS, and Recall. 4) The learned flow is more straight than others, evaluated by curvature. We achieve much lower FID in both one-step and full-step generation in CIFAR-10. The conic reflow generalizes to various datasets such as LSUN Bedroom and ImageNet.