Diff-CL: A Novel Cross Pseudo-Supervision Method for Semi-supervised Medical Image Segmentation

Semi-supervised learning utilizes insights from unlabeled data to improve model generalization, thereby reducing reliance on large labeled datasets. Most existing studies focus on limited samples and fail to capture the overall data distribution. We contend that combining distributional information with detailed information is crucial for achieving more robust and accurate segmentation results. On the one hand, with its robust generative capabilities, diffusion models (DM) learn data distribution effectively. However, it struggles with fine detail capture, leading to generated images with misleading details. Combining DM with convolutional neural networks (CNNs) enables the former to learn data distribution while the latter corrects fine details. While capturing complete high-frequency details by CNNs requires substantial computational resources and is susceptible to local noise. On the other hand, given that both labeled and unlabeled data come from the same distribution, we believe that regions in unlabeled data similar to overall class semantics to labeled data are likely to belong to the same class, while regions with minimal similarity are less likely to. This work introduces a semi-supervised medical image segmentation framework from the distribution perspective (Diff-CL). Firstly, we propose a cross-pseudo-supervision learning mechanism between diffusion and convolution segmentation networks. Secondly, we design a high-frequency mamba module to capture boundary and detail information globally. Finally, we apply contrastive learning for label propagation from labeled to unlabeled data. Our method achieves state-of-the-art (SOTA) performance across three datasets, including left atrium, brain tumor, and NIH pancreas datasets.

Solving Prior Distribution Mismatch in Diffusion Models via Optimal Transport

In recent years, the knowledge surrounding diffusion models(DMs) has grown significantly, though several theoretical gaps remain. Particularly noteworthy is prior error, defined as the discrepancy between the termination distribution of the forward process and the initial distribution of the reverse process. To address these deficiencies, this paper explores the deeper relationship between optimal transport(OT) theory and DMs with discrete initial distribution. Specifically, we demonstrate that the two stages of DMs fundamentally involve computing time-dependent OT. However, unavoidable prior error result in deviation during the reverse process under quadratic transport cost. By proving that as the diffusion termination time increases, the probability flow exponentially converges to the gradient of the solution to the classical Monge-Amp\`ere equation, we establish a vital link between these fields. Therefore, static OT emerges as the most intrinsic single-step method for bridging this theoretical potential gap. Additionally, we apply these insights to accelerate sampling in both unconditional and conditional generation scenarios. Experimental results across multiple image datasets validate the effectiveness of our approach.

HOTS3D: Hyper-Spherical Optimal Transport for Semantic Alignment of Text-to-3D Generation

Recent CLIP-guided 3D generation methods have achieved promising results but struggle with generating faithful 3D shapes that conform with input text due to the gap between text and image embeddings. To this end, this paper proposes HOTS3D which makes the first attempt to effectively bridge this gap by aligning text features to the image features with spherical optimal transport (SOT). However, in high-dimensional situations, solving the SOT remains a challenge. To obtain the SOT map for high-dimensional features obtained from CLIP encoding of two modalities, we mathematically formulate and derive the solution based on Villani's theorem, which can directly align two hyper-sphere distributions without manifold exponential maps. Furthermore, we implement it by leveraging input convex neural networks (ICNNs) for the optimal Kantorovich potential. With the optimally mapped features, a diffusion-based generator and a Nerf-based decoder are subsequently utilized to transform them into 3D shapes. Extensive qualitative and qualitative comparisons with state-of-the-arts demonstrate the superiority of the proposed HOTS3D for 3D shape generation, especially on the consistency with text semantics.

MergeNet: Explicit Mesh Reconstruction from Sparse Point Clouds via Edge Prediction

This paper introduces a novel method for reconstructing meshes from sparse point clouds by predicting edge connection. Existing implicit methods usually produce superior smooth and watertight meshes due to the isosurface extraction algorithms~(e.g., Marching Cubes). However, these methods become memory and computationally intensive with increasing resolution. Explicit methods are more efficient by directly forming the face from points. Nevertheless, the challenge of selecting appropriate faces from enormous candidates often leads to undesirable faces and holes. Moreover, the reconstruction performance of both approaches tends to degrade when the point cloud gets sparse. To this end, we propose MEsh Reconstruction via edGE~(MergeNet), which converts mesh reconstruction into local connectivity prediction problems. Specifically, MergeNet learns to extract the features of candidate edges and regress their distances to the underlying surface. Consequently, the predicted distance is utilized to filter out edges that lay on surfaces. Finally, the meshes are reconstructed by refining the triangulations formed by these edges. Extensive experiments on synthetic and real-scanned datasets demonstrate the superiority of MergeNet to SoTA explicit methods.

Learning Unsigned Distance Fields from Local Shape Functions for 3D Surface Reconstruction

Unsigned distance fields (UDFs) provide a versatile framework for representing a diverse array of 3D shapes, encompassing both watertight and non-watertight geometries. Traditional UDF learning methods typically require extensive training on large datasets of 3D shapes, which is costly and often necessitates hyperparameter adjustments for new datasets. This paper presents a novel neural framework, LoSF-UDF, for reconstructing surfaces from 3D point clouds by leveraging local shape functions to learn UDFs. We observe that 3D shapes manifest simple patterns within localized areas, prompting us to create a training dataset of point cloud patches characterized by mathematical functions that represent a continuum from smooth surfaces to sharp edges and corners. Our approach learns features within a specific radius around each query point and utilizes an attention mechanism to focus on the crucial features for UDF estimation. This method enables efficient and robust surface reconstruction from point clouds without the need for shape-specific training. Additionally, our method exhibits enhanced resilience to noise and outliers in point clouds compared to existing methods. We present comprehensive experiments and comparisons across various datasets, including synthetic and real-scanned point clouds, to validate our method's efficacy.

Global Parameterization-based Texture Space Optimization

Texture mapping is a common technology in the area of computer graphics, it maps the 3D surface space onto the 2D texture space. However, the loose texture space will reduce the efficiency of data storage and GPU memory addressing in the rendering process. Many of the existing methods focus on repacking given textures, but they still suffer from high computational cost and hardly produce a wholly tight texture space. In this paper, we propose a method to optimize the texture space and produce a new texture mapping which is compact based on global parameterization. The proposed method is computationally robust and efficient. Experiments show the effectiveness of the proposed method and the potency in improving the storage and rendering efficiency.

Point Cloud Compression via Constrained Optimal Transport

This paper presents a novel point cloud compression method COT-PCC by formulating the task as a constrained optimal transport (COT) problem. COT-PCC takes the bitrate of compressed features as an extra constraint of optimal transport (OT) which learns the distribution transformation between original and reconstructed points. Specifically, the formulated COT is implemented with a generative adversarial network (GAN) and a bitrate loss for training. The discriminator measures the Wasserstein distance between input and reconstructed points, and a generator calculates the optimal mapping between distributions of input and reconstructed point cloud. Moreover, we introduce a learnable sampling module for downsampling in the compression procedure. Extensive results on both sparse and dense point cloud datasets demonstrate that COT-PCC outperforms state-of-the-art methods in terms of both CD and PSNR metrics. Source codes are available at \url{https://github.com/cognaclee/PCC-COT}.

Topology-Aware Latent Diffusion for 3D Shape Generation

We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves representing 3D shapes as implicit fields, then employing persistent homology to extract topological features, including Betti numbers and persistence diagrams. The shape generation process consists of two steps. Initially, we employ a transformer-based autoencoding module to embed the implicit representation of each 3D shape into a set of latent vectors. Subsequently, we navigate through the learned latent space via a diffusion model. By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures. Furthermore, our framework is flexible, supporting generation tasks constrained by a variety of inputs, including sparse and partial point clouds, as well as sketches. By modifying the persistence diagrams, we can alter the topology of the shapes generated from these input modalities.

DPM-OT: A New Diffusion Probabilistic Model Based on Optimal Transport

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT

OT-Net: A Reusable Neural Optimal Transport Solver

With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel reusable neural OT solver OT-Net is thus presented, which first learns Brenier's height representation via the neural network to obtain its potential, and then gained the OT map by computing the gradient of the potential. The algorithm has two merits, 1) it can easily represent discontinuous maps, which allows it to match any target distribution with discontinuous supports and achieve sharp boundaries. This can well eliminate mode collapse in the generated models. 2) The OT map can be calculated straightly by the proposed algorithm when new target samples are added, which greatly improves the efficiency and reusability of the map. Moreover, the theoretical error bound of the algorithm is analyzed, and we have demonstrated the empirical success of our approach in image generation, color transfer, and domain adaptation.