Score-based diffusion models (SBDMs) have achieved state-of-the-art results in image generation. In this paper, we propose a Non-isotropic Gaussian Diffusion Model (NGDM) for image editing, which requires editing the source image while preserving the image regions irrelevant to the editing task. We construct NGDM by adding independent Gaussian noises with different variances to different image pixels.

We are interested in the computation of the transport map of an Optimal Transport problem. Most of the computational approaches of Optimal Transport use the Kantorovich relaxation of the problem to learn a probabilistic coupling γ but do not address the problem of learning the underlying transport map T linked to the original Monge problem. Consequently, it lowers the potential usage of such methods in contexts where out-of-samples computations are mandatory. In this paper we propose a new way to jointly learn the coupling and an approximation of the transport map. We use a jointly convex formulation which can be efficiently optimized. Additionally, jointly learning the coupling and the transport map allows to smooth the result of the Optimal Transport and generalize it to out-of-samples examples. Empirically, we show the interest and the relevance of our method in two tasks: domain adaptation and image editing.

Text-guided diffusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. We address these challenges by investigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as a key issue. To resolve this, we introduce the, a novel noise schedule designed to eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity compared to traditional noise schedules, highlighting its adaptability and effectiveness. The project page is available at https://lonelvino.github.io/SYE/.

Drag-based image editing using generative models provides precise control over image contents, enabling users to manipulate anything in an image with a few clicks. However, prevailing methods typically adopt $n$-step iterations for latent semantic optimization to achieve drag-based image editing, which is time-consuming and limits practical applications. In this paper, we introduce a novel one-step drag-based image editing method, i.e., FastDrag, to accelerate the editing process. Central to our approach is a latent warpage function (LWF), which simulates the behavior of a stretched material to adjust the location of individual pixels within the latent space. This innovation achieves one-step latent semantic optimization and hence significantly promotes editing speeds. Meanwhile, null regions emerging after applying LWF are addressed by our proposed bilateral nearest neighbor interpolation (BNNI) strategy.

In image editing, Denoising Diffusion Implicit Models (DDIM) inversion has become a widely adopted method and is extensively used in various image editing approaches. The core concept of DDIM inversion stems from the deterministic sampling technique of DDIM, which allows the DDIM process to be viewed as an Ordinary Differential Equation (ODE) process that is reversible. This enables the prediction of corresponding noise from a reference image, ensuring that the restored image from this noise remains consistent with the reference image. Image editing exploits this property by modifying the cross-attention between text and images to edit specific objects while preserving the remaining regions. However, in the DDIM inversion, using the $t-1$ time step to approximate the noise prediction at time step $t$ introduces errors between the restored image and the reference image.

Harmony (A TIH) to generate novel and surprising objects.

For image editing, it also excels in complex editing tasks. 2 Therefore, it is nearly impossible for a well-trained model to meet all human requirements, and the