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Sep 1

DCPI-Depth: Explicitly Infusing Dense Correspondence Prior to Unsupervised Monocular Depth Estimation

There has been a recent surge of interest in learning to perceive depth from monocular videos in an unsupervised fashion. A key challenge in this field is achieving robust and accurate depth estimation in challenging scenarios, particularly in regions with weak textures or where dynamic objects are present. This study makes three major contributions by delving deeply into dense correspondence priors to provide existing frameworks with explicit geometric constraints. The first novelty is a contextual-geometric depth consistency loss, which employs depth maps triangulated from dense correspondences based on estimated ego-motion to guide the learning of depth perception from contextual information, since explicitly triangulated depth maps capture accurate relative distances among pixels. The second novelty arises from the observation that there exists an explicit, deducible relationship between optical flow divergence and depth gradient. A differential property correlation loss is, therefore, designed to refine depth estimation with a specific emphasis on local variations. The third novelty is a bidirectional stream co-adjustment strategy that enhances the interaction between rigid and optical flows, encouraging the former towards more accurate correspondence and making the latter more adaptable across various scenarios under the static scene hypotheses. DCPI-Depth, a framework that incorporates all these innovative components and couples two bidirectional and collaborative streams, achieves state-of-the-art performance and generalizability across multiple public datasets, outperforming all existing prior arts. Specifically, it demonstrates accurate depth estimation in texture-less and dynamic regions, and shows more reasonable smoothness. Our source code will be publicly available at mias.group/DCPI-Depth upon publication.

  • 4 authors
·
May 27, 2024

CasP: Improving Semi-Dense Feature Matching Pipeline Leveraging Cascaded Correspondence Priors for Guidance

Semi-dense feature matching methods have shown strong performance in challenging scenarios. However, the existing pipeline relies on a global search across the entire feature map to establish coarse matches, limiting further improvements in accuracy and efficiency. Motivated by this limitation, we propose a novel pipeline, CasP, which leverages cascaded correspondence priors for guidance. Specifically, the matching stage is decomposed into two progressive phases, bridged by a region-based selective cross-attention mechanism designed to enhance feature discriminability. In the second phase, one-to-one matches are determined by restricting the search range to the one-to-many prior areas identified in the first phase. Additionally, this pipeline benefits from incorporating high-level features, which helps reduce the computational costs of low-level feature extraction. The acceleration gains of CasP increase with higher resolution, and our lite model achieves a speedup of sim2.2times at a resolution of 1152 compared to the most efficient method, ELoFTR. Furthermore, extensive experiments demonstrate its superiority in geometric estimation, particularly with impressive cross-domain generalization. These advantages highlight its potential for latency-sensitive and high-robustness applications, such as SLAM and UAV systems. Code is available at https://github.com/pq-chen/CasP.

  • 12 authors
·
Jul 23, 2025

Self-supervised Learning of Implicit Shape Representation with Dense Correspondence for Deformable Objects

Learning 3D shape representation with dense correspondence for deformable objects is a fundamental problem in computer vision. Existing approaches often need additional annotations of specific semantic domain, e.g., skeleton poses for human bodies or animals, which require extra annotation effort and suffer from error accumulation, and they are limited to specific domain. In this paper, we propose a novel self-supervised approach to learn neural implicit shape representation for deformable objects, which can represent shapes with a template shape and dense correspondence in 3D. Our method does not require the priors of skeleton and skinning weight, and only requires a collection of shapes represented in signed distance fields. To handle the large deformation, we constrain the learned template shape in the same latent space with the training shapes, design a new formulation of local rigid constraint that enforces rigid transformation in local region and addresses local reflection issue, and present a new hierarchical rigid constraint to reduce the ambiguity due to the joint learning of template shape and correspondences. Extensive experiments show that our model can represent shapes with large deformations. We also show that our shape representation can support two typical applications, such as texture transfer and shape editing, with competitive performance. The code and models are available at https://iscas3dv.github.io/deformshape

  • 6 authors
·
Aug 24, 2023

FramePainter: Endowing Interactive Image Editing with Video Diffusion Priors

Interactive image editing allows users to modify images through visual interaction operations such as drawing, clicking, and dragging. Existing methods construct such supervision signals from videos, as they capture how objects change with various physical interactions. However, these models are usually built upon text-to-image diffusion models, so necessitate (i) massive training samples and (ii) an additional reference encoder to learn real-world dynamics and visual consistency. In this paper, we reformulate this task as an image-to-video generation problem, so that inherit powerful video diffusion priors to reduce training costs and ensure temporal consistency. Specifically, we introduce FramePainter as an efficient instantiation of this formulation. Initialized with Stable Video Diffusion, it only uses a lightweight sparse control encoder to inject editing signals. Considering the limitations of temporal attention in handling large motion between two frames, we further propose matching attention to enlarge the receptive field while encouraging dense correspondence between edited and source image tokens. We highlight the effectiveness and efficiency of FramePainter across various of editing signals: it domainantly outperforms previous state-of-the-art methods with far less training data, achieving highly seamless and coherent editing of images, \eg, automatically adjust the reflection of the cup. Moreover, FramePainter also exhibits exceptional generalization in scenarios not present in real-world videos, \eg, transform the clownfish into shark-like shape. Our code will be available at https://github.com/YBYBZhang/FramePainter.

  • 6 authors
·
Jan 14, 2025 2

Diffusion Model for Dense Matching

The objective for establishing dense correspondence between paired images consists of two terms: a data term and a prior term. While conventional techniques focused on defining hand-designed prior terms, which are difficult to formulate, recent approaches have focused on learning the data term with deep neural networks without explicitly modeling the prior, assuming that the model itself has the capacity to learn an optimal prior from a large-scale dataset. The performance improvement was obvious, however, they often fail to address inherent ambiguities of matching, such as textureless regions, repetitive patterns, and large displacements. To address this, we propose DiffMatch, a novel conditional diffusion-based framework designed to explicitly model both the data and prior terms. Unlike previous approaches, this is accomplished by leveraging a conditional denoising diffusion model. DiffMatch consists of two main components: conditional denoising diffusion module and cost injection module. We stabilize the training process and reduce memory usage with a stage-wise training strategy. Furthermore, to boost performance, we introduce an inference technique that finds a better path to the accurate matching field. Our experimental results demonstrate significant performance improvements of our method over existing approaches, and the ablation studies validate our design choices along with the effectiveness of each component. Project page is available at https://ku-cvlab.github.io/DiffMatch/.

  • 7 authors
·
May 30, 2023

DenseGAP: Graph-Structured Dense Correspondence Learning with Anchor Points

Establishing dense correspondence between two images is a fundamental computer vision problem, which is typically tackled by matching local feature descriptors. However, without global awareness, such local features are often insufficient for disambiguating similar regions. And computing the pairwise feature correlation across images is both computation-expensive and memory-intensive. To make the local features aware of the global context and improve their matching accuracy, we introduce DenseGAP, a new solution for efficient Dense correspondence learning with a Graph-structured neural network conditioned on Anchor Points. Specifically, we first propose a graph structure that utilizes anchor points to provide sparse but reliable prior on inter- and intra-image context and propagates them to all image points via directed edges. We also design a graph-structured network to broadcast multi-level contexts via light-weighted message-passing layers and generate high-resolution feature maps at low memory cost. Finally, based on the predicted feature maps, we introduce a coarse-to-fine framework for accurate correspondence prediction using cycle consistency. Our feature descriptors capture both local and global information, thus enabling a continuous feature field for querying arbitrary points at high resolution. Through comprehensive ablative experiments and evaluations on large-scale indoor and outdoor datasets, we demonstrate that our method advances the state-of-the-art of correspondence learning on most benchmarks.

  • 5 authors
·
Dec 13, 2021

HomoMatcher: Dense Feature Matching Results with Semi-Dense Efficiency by Homography Estimation

Feature matching between image pairs is a fundamental problem in computer vision that drives many applications, such as SLAM. Recently, semi-dense matching approaches have achieved substantial performance enhancements and established a widely-accepted coarse-to-fine paradigm. However, the majority of existing methods focus on improving coarse feature representation rather than the fine-matching module. Prior fine-matching techniques, which rely on point-to-patch matching probability expectation or direct regression, often lack precision and do not guarantee the continuity of feature points across sequential images. To address this limitation, this paper concentrates on enhancing the fine-matching module in the semi-dense matching framework. We employ a lightweight and efficient homography estimation network to generate the perspective mapping between patches obtained from coarse matching. This patch-to-patch approach achieves the overall alignment of two patches, resulting in a higher sub-pixel accuracy by incorporating additional constraints. By leveraging the homography estimation between patches, we can achieve a dense matching result with low computational cost. Extensive experiments demonstrate that our method achieves higher accuracy compared to previous semi-dense matchers. Meanwhile, our dense matching results exhibit similar end-point-error accuracy compared to previous dense matchers while maintaining semi-dense efficiency.

  • 9 authors
·
Nov 10, 2024

Geometry Matters: 3D Foundation Priors for Learning Semantic Correspondence

Foundation features from self-supervised vision models and text-to-image diffusion models have proven effective for semantic correspondence estimation. However, because these features are learned primarily from 2D image objectives, they lack explicit 3D awareness and often confuse symmetric object sides, repeated parts, and visually similar structures that are distinct in 3D. We introduce a 3D-aware post-training framework that goes beyond available 2D foundation features by incorporating priors from 3D foundation models. Given an image, our method uses SAM3D to estimate object geometry and pose, and refines the pose through render-and-compare optimization. Subsequently, we render PartField descriptors from the reconstructed geometry into the image plane based on the estimated object pose. The resulting geometry-aware feature maps complement DINO and Stable Diffusion features, while geodesic distances on the reconstructed shapes enable reliable filtering of candidate correspondences. We use the filtered matches as supervision to train a lightweight adapter on top of DINO and Stable Diffusion for semantic correspondence. In contrast to prior post-training approaches that require pose annotations and rely on coarse spherical geometry, our method automatically obtains instance-specific 3D structure and uses it to guide correspondence learning. Experiments show that our approach improves semantic correspondence over the prior methods while reducing manual geometric supervision. Code and model can be found at https:/github.com/GenIntel/3D-SC.

Distillation of Diffusion Features for Semantic Correspondence

Semantic correspondence, the task of determining relationships between different parts of images, underpins various applications including 3D reconstruction, image-to-image translation, object tracking, and visual place recognition. Recent studies have begun to explore representations learned in large generative image models for semantic correspondence, demonstrating promising results. Building on this progress, current state-of-the-art methods rely on combining multiple large models, resulting in high computational demands and reduced efficiency. In this work, we address this challenge by proposing a more computationally efficient approach. We propose a novel knowledge distillation technique to overcome the problem of reduced efficiency. We show how to use two large vision foundation models and distill the capabilities of these complementary models into one smaller model that maintains high accuracy at reduced computational cost. Furthermore, we demonstrate that by incorporating 3D data, we are able to further improve performance, without the need for human-annotated correspondences. Overall, our empirical results demonstrate that our distilled model with 3D data augmentation achieves performance superior to current state-of-the-art methods while significantly reducing computational load and enhancing practicality for real-world applications, such as semantic video correspondence. Our code and weights are publicly available on our project page.

  • 4 authors
·
Dec 4, 2024

Robust Outlier Rejection for 3D Registration with Variational Bayes

Learning-based outlier (mismatched correspondence) rejection for robust 3D registration generally formulates the outlier removal as an inlier/outlier classification problem. The core for this to be successful is to learn the discriminative inlier/outlier feature representations. In this paper, we develop a novel variational non-local network-based outlier rejection framework for robust alignment. By reformulating the non-local feature learning with variational Bayesian inference, the Bayesian-driven long-range dependencies can be modeled to aggregate discriminative geometric context information for inlier/outlier distinction. Specifically, to achieve such Bayesian-driven contextual dependencies, each query/key/value component in our non-local network predicts a prior feature distribution and a posterior one. Embedded with the inlier/outlier label, the posterior feature distribution is label-dependent and discriminative. Thus, pushing the prior to be close to the discriminative posterior in the training step enables the features sampled from this prior at test time to model high-quality long-range dependencies. Notably, to achieve effective posterior feature guidance, a specific probabilistic graphical model is designed over our non-local model, which lets us derive a variational low bound as our optimization objective for model training. Finally, we propose a voting-based inlier searching strategy to cluster the high-quality hypothetical inliers for transformation estimation. Extensive experiments on 3DMatch, 3DLoMatch, and KITTI datasets verify the effectiveness of our method.

  • 6 authors
·
Apr 3, 2023

Grounding Image Matching in 3D with MASt3R

Image Matching is a core component of all best-performing algorithms and pipelines in 3D vision. Yet despite matching being fundamentally a 3D problem, intrinsically linked to camera pose and scene geometry, it is typically treated as a 2D problem. This makes sense as the goal of matching is to establish correspondences between 2D pixel fields, but also seems like a potentially hazardous choice. In this work, we take a different stance and propose to cast matching as a 3D task with DUSt3R, a recent and powerful 3D reconstruction framework based on Transformers. Based on pointmaps regression, this method displayed impressive robustness in matching views with extreme viewpoint changes, yet with limited accuracy. We aim here to improve the matching capabilities of such an approach while preserving its robustness. We thus propose to augment the DUSt3R network with a new head that outputs dense local features, trained with an additional matching loss. We further address the issue of quadratic complexity of dense matching, which becomes prohibitively slow for downstream applications if not carefully treated. We introduce a fast reciprocal matching scheme that not only accelerates matching by orders of magnitude, but also comes with theoretical guarantees and, lastly, yields improved results. Extensive experiments show that our approach, coined MASt3R, significantly outperforms the state of the art on multiple matching tasks. In particular, it beats the best published methods by 30% (absolute improvement) in VCRE AUC on the extremely challenging Map-free localization dataset.

  • 3 authors
·
Jun 14, 2024

Training-Free Diffusion Priors for Text-to-Image Generation via Optimization-based Visual Inversion

Diffusion models have established the state-of-the-art in text-to-image generation, but their performance often relies on a diffusion prior network to translate text embeddings into the visual manifold for easier decoding. These priors are computationally expensive and require extensive training on massive datasets. In this work, we challenge the necessity of a trained prior at all by employing Optimization-based Visual Inversion (OVI), a training-free and zero-shot alternative, to replace the need for a prior. OVI initializes a latent visual representation from random pseudo-tokens and iteratively optimizes it to maximize the cosine similarity with the input textual prompt embedding. We further propose two novel constraints, a Mahalanobis-based and a Nearest-Neighbor loss, to regularize the OVI optimization process toward the distribution of realistic images. Our experiments, conducted on Kandinsky 2.2, show that OVI can serve as an alternative to traditional priors. More importantly, our analysis reveals a critical flaw in current evaluation benchmarks like T2I-CompBench++, where simply using the text embedding as a prior achieves surprisingly high scores, despite lower perceptual quality. Our constrained OVI methods improve visual fidelity over this baseline, with the Nearest-Neighbor approach proving particularly effective. It achieves quantitative scores comparable to or higher than the state-of-the-art data-efficient prior, underscoring the potential of optimization-based strategies as viable, training-free alternatives to traditional priors. The code will be publicly available upon acceptance.

  • 2 authors
·
Dec 26, 2025

Category-Level 3D Correspondence in Camera Space via Morphable Object Priors

Understanding 3D objects from images is fundamental to robotics and AR/VR applications. While recent work has made progress in category-level pose estimation, current representations fail to capture the fine-grained semantics needed for reasoning about object parts, functions, and interactions. In this work, we study category-level 3D correspondence in camera space -- predicting, from a single image, 3D locations that remain consistent across instances within a category -- and show that it can emerge without explicit correspondence supervision by learning a shared morphable object prior. To enable research in this direction, we introduce HouseCorr3D, the first large-scale benchmark for monocular category-level 3D correspondence with 178k images across 50 household object categories, 280 unique instances, and 3D keypoint annotations directly on CAD models. Crucially, HouseCorr3D provides amodal correspondence labels for occluded regions and explicit symmetry annotations, addressing key limitations of existing datasets. We further propose Morpheus, a method that learns morphable category-level shape priors by disentangling canonical shape, deformation, and object pose. Through this shared canonical grounding, semantically meaningful 3D correspondences in camera space emerge implicitly. These emerging 3D correspondences set a new state of the art on HouseCorr3D, demonstrating that semantic 3D object understanding can arise without direct correspondence supervision. Data and code are publicly available at https://github.com/GenIntel/HouseCorr3D.

Prioritizing Image-Related Tokens Enhances Vision-Language Pre-Training

In standard large vision-language models (LVLMs) pre-training, the model typically maximizes the joint probability of the caption conditioned on the image via next-token prediction (NTP); however, since only a small subset of caption tokens directly relates to the visual content, this naive NTP unintentionally fits the model to noise and increases the risk of hallucination. We present PRIOR, a simple vision-language pre-training approach that addresses this issue by prioritizing image-related tokens through differential weighting in the NTP loss, drawing from the importance sampling framework. PRIOR introduces a reference model-a text-only large language model (LLM) trained on the captions without image inputs, to weight each token based on its probability for LVLMs training. Intuitively, tokens that are directly related to the visual inputs are harder to predict without the image and thus receive lower probabilities from the text-only reference LLM. During training, we implement a token-specific re-weighting term based on the importance scores to adjust each token's loss. We implement PRIOR in two distinct settings: LVLMs with visual encoders and LVLMs without visual encoders. We observe 19% and 8% average relative improvement, respectively, on several vision-language benchmarks compared to NTP. In addition, PRIOR exhibits superior scaling properties, as demonstrated by significantly higher scaling coefficients, indicating greater potential for performance gains compared to NTP given increasing compute and data.

  • 4 authors
·
May 13, 2025

Unified Multivariate Gaussian Mixture for Efficient Neural Image Compression

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.

  • 5 authors
·
Mar 21, 2022

Rethinking Few-Shot Image Fusion: Granular Ball Priors Enable General-Purpose Deep Fusion

In image fusion tasks, the absence of real fused images as supervision signals poses significant challenges for supervised learning. Existing deep learning methods typically address this issue either by designing handcrafted priors or by relying on large-scale datasets to learn model parameters. Different from previous approaches, this paper introduces the concept of incomplete priors, which formally describe handcrafted priors at the algorithmic level and estimate their confidence. Based on this idea, we couple incomplete priors with the neural network through a sample-level adaptive loss function, enabling the network to learn and re-infer fusion rules under conditions that approximate the real fusion process.To generate incomplete priors, we propose a Granular Ball Pixel Computation (GBPC) algorithm based on the principles of granular computing. The algorithm models fused-image pixels as information units, estimating pixel weights at a fine-grained level while statistically evaluating prior reliability at a coarse-grained level. This design enables the algorithm to perceive cross-modal discrepancies and perform adaptive inference.Experimental results demonstrate that even under few-shot conditions, a lightweight neural network can still learn effective fusion rules by training only on image patches extracted from ten image pairs. Extensive experiments across multiple fusion tasks and datasets further show that the proposed method achieves superior performance in both visual quality and model compactness. The code is available at: https://github.com/DMinjie/GBFF

  • 6 authors
·
Apr 11, 2025

NoPA: Non-Parametric Online 3D Scene Graph Generation

Classic 3D scene graph generation approaches fail to work in real-time due to the heavy computational cost of environment mapping and the need to generate intermediate point-cloud representations. To alleviate this issue, a recent work eschews point clouds in favor of a lightweight Gaussian distribution for each object. This approximation drastically speeds up inference and enables real-time 3D scene graph generation. However, the representation has two key weaknesses. 1) Each object is approximated by a single 3D Gaussian, which causes a severe loss of 3D geometric detail. 2) The discrepancy between this approximation and the true object geometry exacerbates the inaccurate merging of object candidates during online inference. To address these issues, we propose NoPA, which represents each object as a separate non-parametric distribution. This formulation retains 3D geometric information while preserving real-time inference of the parametric Gaussian formulation. To build upon our novel object representation, we propose a tailored merging strategy to recover coherent object instances. Specifically, we leverage maximum mean discrepancy on kernel density estimates to enable robust merging of object candidates during online exploration while minimizing added computational complexity. The key is to maintain a fixed particle set per object. Furthermore, to rectify the relation loss caused by misclassified objects, NoPA propagates relationships between objects with high affinity. Experiments show that NoPA substantially outperforms current methods without sacrificing real-time inference speed.

SOCO: Benchmarking Semantic Object Correspondence in Vision Foundation Models

Measuring structured object understanding in vision foundation models remains challenging due to inconsistent evaluation protocols and limited part-level supervision. Semantic correspondence (SC) evaluates this capability by testing whether object parts can be matched across instances and categories under large variations in appearance, viewpoint, and geometry. To enable a systematic SC evaluation, we introduce SOCO, a new benchmark for Semantic Object Correspondence that introduces a taxonomy of correspondence types and provides consistent, functionally meaningful keypoint annotations across 100 categories and over 1M correspondence pairs. In addition, SOCO includes keypoint language descriptions, enabling the evaluation of large vision-language models (LVLMs) and their fine-grained part-level understanding. Comprehensive experiments reveal that (i) vision foundation backbones encode strong semantic structure but transfer correspondences poorly across related categories and only partially capture object-part position, (ii) LVLMs are stronger at text-prompted part localization than at visual-reference cross-image matching, exposing a gap between language-grounded localization and fine-grained visual correspondence, and (iii) correspondence performance predicts performance on dense downstream tasks, including segmentation, tracking, 3D pose estimation, and 3D detection, more strongly than ImageNet classification. Together, these findings position SOCO as a benchmark for structured, part-level representation quality in vision and multimodal foundation models.

Beyond 3D VQAs: Injecting 3D Spatial Priors into Vision-Language Models for Enhanced Geometric Reasoning

Vision-Language Models (VLMs) often struggle with robust 3D spatial reasoning. Prevailing methods that rely on fine-tuning with 3D visual question-answering (VQA) datasets may overfit dataset-specific biases, while integrating specialized 3D visual encoders is often inflexible and cumbersome. In this paper, we argue that genuine spatial understanding should emerge from learning fundamental geometric priors, not only from high-level VQA supervision. We propose GASP (Geometric-Aware Spatial Priors), a framework that injects these priors directly into the LLM's transformer layers. GASP employs a small correspondence head, applied as a deep supervision signal across all layers, and is trained with a dual objective leveraging ground-truth geometry from large-scale video scenes: a contrastive loss on ground-truth point correspondences enforces 2D view-invariance, while a depth consistency supervision resolves 3D geometric ambiguities. Our analysis first provides a diagnostic showing that standard VLMs' internal correspondence matching accuracy is very low (often below 5%). We then demonstrate that our training substantially improves this behavior, boosting peak layer-wise correspondence to over 70% and maintaining over 85% temporal robustness while baselines remain below 5%. These internal improvements translate to significant gains on downstream spatial benchmarks including +18.2% on All-Angles Bench and +29.0% on VSI-Bench, all without training on any 3D VQA data. Our findings indicate that learning from fundamental geometric priors is a promising and generalizable pathway towards VLMs with more reliable 3D spatial reasoning.

  • 6 authors
·
May 27 1

SweetDreamer: Aligning Geometric Priors in 2D Diffusion for Consistent Text-to-3D

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

  • 4 authors
·
Oct 4, 2023

Homeomorphism Prior for False Positive and Negative Problem in Medical Image Dense Contrastive Representation Learning

Dense contrastive representation learning (DCRL) has greatly improved the learning efficiency for image-dense prediction tasks, showing its great potential to reduce the large costs of medical image collection and dense annotation. However, the properties of medical images make unreliable correspondence discovery, bringing an open problem of large-scale false positive and negative (FP&N) pairs in DCRL. In this paper, we propose GEoMetric vIsual deNse sImilarity (GEMINI) learning which embeds the homeomorphism prior to DCRL and enables a reliable correspondence discovery for effective dense contrast. We propose a deformable homeomorphism learning (DHL) which models the homeomorphism of medical images and learns to estimate a deformable mapping to predict the pixels' correspondence under topological preservation. It effectively reduces the searching space of pairing and drives an implicit and soft learning of negative pairs via a gradient. We also propose a geometric semantic similarity (GSS) which extracts semantic information in features to measure the alignment degree for the correspondence learning. It will promote the learning efficiency and performance of deformation, constructing positive pairs reliably. We implement two practical variants on two typical representation learning tasks in our experiments. Our promising results on seven datasets which outperform the existing methods show our great superiority. We will release our code on a companion link: https://github.com/YutingHe-list/GEMINI.

  • 6 authors
·
Feb 7, 2025 2

Zero-Shot 3D Shape Correspondence

We propose a novel zero-shot approach to computing correspondences between 3D shapes. Existing approaches mainly focus on isometric and near-isometric shape pairs (e.g., human vs. human), but less attention has been given to strongly non-isometric and inter-class shape matching (e.g., human vs. cow). To this end, we introduce a fully automatic method that exploits the exceptional reasoning capabilities of recent foundation models in language and vision to tackle difficult shape correspondence problems. Our approach comprises multiple stages. First, we classify the 3D shapes in a zero-shot manner by feeding rendered shape views to a language-vision model (e.g., BLIP2) to generate a list of class proposals per shape. These proposals are unified into a single class per shape by employing the reasoning capabilities of ChatGPT. Second, we attempt to segment the two shapes in a zero-shot manner, but in contrast to the co-segmentation problem, we do not require a mutual set of semantic regions. Instead, we propose to exploit the in-context learning capabilities of ChatGPT to generate two different sets of semantic regions for each shape and a semantic mapping between them. This enables our approach to match strongly non-isometric shapes with significant differences in geometric structure. Finally, we employ the generated semantic mapping to produce coarse correspondences that can further be refined by the functional maps framework to produce dense point-to-point maps. Our approach, despite its simplicity, produces highly plausible results in a zero-shot manner, especially between strongly non-isometric shapes.

  • 4 authors
·
Jun 5, 2023

Transformers Can Do Bayesian Inference

Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs leverage large-scale machine learning techniques to approximate a large set of posteriors. The only requirement for PFNs to work is the ability to sample from a prior distribution over supervised learning tasks (or functions). Our method restates the objective of posterior approximation as a supervised classification problem with a set-valued input: it repeatedly draws a task (or function) from the prior, draws a set of data points and their labels from it, masks one of the labels and learns to make probabilistic predictions for it based on the set-valued input of the rest of the data points. Presented with a set of samples from a new supervised learning task as input, PFNs make probabilistic predictions for arbitrary other data points in a single forward propagation, having learned to approximate Bayesian inference. We demonstrate that PFNs can near-perfectly mimic Gaussian processes and also enable efficient Bayesian inference for intractable problems, with over 200-fold speedups in multiple setups compared to current methods. We obtain strong results in very diverse areas such as Gaussian process regression, Bayesian neural networks, classification for small tabular data sets, and few-shot image classification, demonstrating the generality of PFNs. Code and trained PFNs are released at https://github.com/automl/TransformersCanDoBayesianInference.

  • 5 authors
·
Dec 20, 2021

CheckerPose: Progressive Dense Keypoint Localization for Object Pose Estimation with Graph Neural Network

Estimating the 6-DoF pose of a rigid object from a single RGB image is a crucial yet challenging task. Recent studies have shown the great potential of dense correspondence-based solutions, yet improvements are still needed to reach practical deployment. In this paper, we propose a novel pose estimation algorithm named CheckerPose, which improves on three main aspects. Firstly, CheckerPose densely samples 3D keypoints from the surface of the 3D object and finds their 2D correspondences progressively in the 2D image. Compared to previous solutions that conduct dense sampling in the image space, our strategy enables the correspondence searching in a 2D grid (i.e., pixel coordinate). Secondly, for our 3D-to-2D correspondence, we design a compact binary code representation for 2D image locations. This representation not only allows for progressive correspondence refinement but also converts the correspondence regression to a more efficient classification problem. Thirdly, we adopt a graph neural network to explicitly model the interactions among the sampled 3D keypoints, further boosting the reliability and accuracy of the correspondences. Together, these novel components make CheckerPose a strong pose estimation algorithm. When evaluated on the popular Linemod, Linemod-O, and YCB-V object pose estimation benchmarks, CheckerPose clearly boosts the accuracy of correspondence-based methods and achieves state-of-the-art performances. Code is available at https://github.com/RuyiLian/CheckerPose.

  • 2 authors
·
Mar 29, 2023

Diving into the Fusion of Monocular Priors for Generalized Stereo Matching

The matching formulation makes it naturally hard for the stereo matching to handle ill-posed regions like occlusions and non-Lambertian surfaces. Fusing monocular priors has been proven helpful for ill-posed matching, but the biased monocular prior learned from small stereo datasets constrains the generalization. Recently, stereo matching has progressed by leveraging the unbiased monocular prior from the vision foundation model (VFM) to improve the generalization in ill-posed regions. We dive into the fusion process and observe three main problems limiting the fusion of the VFM monocular prior. The first problem is the misalignment between affine-invariant relative monocular depth and absolute depth of disparity. Besides, when we use the monocular feature in an iterative update structure, the over-confidence in the disparity update leads to local optima results. A direct fusion of a monocular depth map could alleviate the local optima problem, but noisy disparity results computed at the first several iterations will misguide the fusion. In this paper, we propose a binary local ordering map to guide the fusion, which converts the depth map into a binary relative format, unifying the relative and absolute depth representation. The computed local ordering map is also used to re-weight the initial disparity update, resolving the local optima and noisy problem. In addition, we formulate the final direct fusion of monocular depth to the disparity as a registration problem, where a pixel-wise linear regression module can globally and adaptively align them. Our method fully exploits the monocular prior to support stereo matching results effectively and efficiently. We significantly improve the performance from the experiments when generalizing from SceneFlow to Middlebury and Booster datasets while barely reducing the efficiency.

  • 6 authors
·
May 20, 2025

Learning 3D Human Shape and Pose from Dense Body Parts

Reconstructing 3D human shape and pose from monocular images is challenging despite the promising results achieved by the most recent learning-based methods. The commonly occurred misalignment comes from the facts that the mapping from images to the model space is highly non-linear and the rotation-based pose representation of body models is prone to result in the drift of joint positions. In this work, we investigate learning 3D human shape and pose from dense correspondences of body parts and propose a Decompose-and-aggregate Network (DaNet) to address these issues. DaNet adopts the dense correspondence maps, which densely build a bridge between 2D pixels and 3D vertices, as intermediate representations to facilitate the learning of 2D-to-3D mapping. The prediction modules of DaNet are decomposed into one global stream and multiple local streams to enable global and fine-grained perceptions for the shape and pose predictions, respectively. Messages from local streams are further aggregated to enhance the robust prediction of the rotation-based poses, where a position-aided rotation feature refinement strategy is proposed to exploit spatial relationships between body joints. Moreover, a Part-based Dropout (PartDrop) strategy is introduced to drop out dense information from intermediate representations during training, encouraging the network to focus on more complementary body parts as well as neighboring position features. The efficacy of the proposed method is validated on both indoor and real-world datasets including Human3.6M, UP3D, COCO, and 3DPW, showing that our method could significantly improve the reconstruction performance in comparison with previous state-of-the-art methods. Our code is publicly available at https://hongwenzhang.github.io/dense2mesh .

  • 5 authors
·
Dec 31, 2019

LoRetta: A Foundation Model and Extensive Dataset for Global-Scale Remote Sensing Dense Image Matching

Dense image matching establishes pixel-wise correspondences and underpins broad applications in computer vision and photogrammetry. However, extending dense matching to global-scale remote sensing remains challenging because image pairs may differ in acquisition time, season, viewpoint, spatial resolution, and land-cover state. The resulting large geometric offsets, partial overlap, and intrinsically unmatchable regions make direct dense correspondence prediction unreliable and inefficient. We thus reformulate dense matching as localization-and-registration: first localizing the matchable overlap and affine geometry, then refining dense residuals within the aligned frame. Based on this formulation, we propose LoRetta, a foundation model coupling matchability-aware affine localization with guided dense registration. We also introduce LEVIR-GM, a global-scale multi-temporal optical matching benchmark with dataset-native matchability labels (103K aligned, 827K augmented pairs, six continents, five years, 0.5-1024 m resolution). We further establish a unified evaluation protocol for sparse, semi-dense, and dense matchers. On LEVIR-GM, LoRetta achieves an area under the curve (AUC) of 83.3%, outperforming the strongest baseline RoMa v2 by 1.6 points, with larger percentage of correct keypoints (PCK) gains of 6.5 and 8.2 points at 1 and 2 pixels, while reducing inference latency by 47.8%. Astronaut-to-satellite and unmanned aerial vehicle (UAV)-to-satellite geolocalization experiments further demonstrate its transferability as a reusable geometric aligner.

  • 4 authors
·
Aug 3

From Editor to Dense Geometry Estimator

Leveraging visual priors from pre-trained text-to-image (T2I) generative models has shown success in dense prediction. However, dense prediction is inherently an image-to-image task, suggesting that image editing models, rather than T2I generative models, may be a more suitable foundation for fine-tuning. Motivated by this, we conduct a systematic analysis of the fine-tuning behaviors of both editors and generators for dense geometry estimation. Our findings show that editing models possess inherent structural priors, which enable them to converge more stably by ``refining" their innate features, and ultimately achieve higher performance than their generative counterparts. Based on these findings, we introduce FE2E, a framework that pioneeringly adapts an advanced editing model based on Diffusion Transformer (DiT) architecture for dense geometry prediction. Specifically, to tailor the editor for this deterministic task, we reformulate the editor's original flow matching loss into the ``consistent velocity" training objective. And we use logarithmic quantization to resolve the precision conflict between the editor's native BFloat16 format and the high precision demand of our tasks. Additionally, we leverage the DiT's global attention for a cost-free joint estimation of depth and normals in a single forward pass, enabling their supervisory signals to mutually enhance each other. Without scaling up the training data, FE2E achieves impressive performance improvements in zero-shot monocular depth and normal estimation across multiple datasets. Notably, it achieves over 35\% performance gains on the ETH3D dataset and outperforms the DepthAnything series, which is trained on 100times data. The project page can be accessed https://amap-ml.github.io/FE2E/{here}.

  • 9 authors
·
Sep 4, 2025 5

All You Need is a Good Functional Prior for Bayesian Deep Learning

The Bayesian treatment of neural networks dictates that a prior distribution is specified over their weight and bias parameters. This poses a challenge because modern neural networks are characterized by a large number of parameters, and the choice of these priors has an uncontrolled effect on the induced functional prior, which is the distribution of the functions obtained by sampling the parameters from their prior distribution. We argue that this is a hugely limiting aspect of Bayesian deep learning, and this work tackles this limitation in a practical and effective way. Our proposal is to reason in terms of functional priors, which are easier to elicit, and to "tune" the priors of neural network parameters in a way that they reflect such functional priors. Gaussian processes offer a rigorous framework to define prior distributions over functions, and we propose a novel and robust framework to match their prior with the functional prior of neural networks based on the minimization of their Wasserstein distance. We provide vast experimental evidence that coupling these priors with scalable Markov chain Monte Carlo sampling offers systematically large performance improvements over alternative choices of priors and state-of-the-art approximate Bayesian deep learning approaches. We consider this work a considerable step in the direction of making the long-standing challenge of carrying out a fully Bayesian treatment of neural networks, including convolutional neural networks, a concrete possibility.

  • 4 authors
·
Nov 25, 2020

Transfer of Representations to Video Label Propagation: Implementation Factors Matter

This work studies feature representations for dense label propagation in video, with a focus on recently proposed methods that learn video correspondence using self-supervised signals such as colorization or temporal cycle consistency. In the literature, these methods have been evaluated with an array of inconsistent settings, making it difficult to discern trends or compare performance fairly. Starting with a unified formulation of the label propagation algorithm that encompasses most existing variations, we systematically study the impact of important implementation factors in feature extraction and label propagation. Along the way, we report the accuracies of properly tuned supervised and unsupervised still image baselines, which are higher than those found in previous works. We also demonstrate that augmenting video-based correspondence cues with still-image-based ones can further improve performance. We then attempt a fair comparison of recent video-based methods on the DAVIS benchmark, showing convergence of best methods to performance levels near our strong ImageNet baseline, despite the usage of a variety of specialized video-based losses and training particulars. Additional comparisons on JHMDB and VIP datasets confirm the similar performance of current methods. We hope that this study will help to improve evaluation practices and better inform future research directions in temporal correspondence.

  • 6 authors
·
Mar 10, 2022

LoMa: Local Feature Matching Revisited

Local feature matching has long been a fundamental component of 3D vision systems such as Structure-from-Motion (SfM), yet progress has lagged behind the rapid advances of modern data-driven approaches. The newer approaches, such as feed-forward reconstruction models, have benefited extensively from scaling dataset sizes, whereas local feature matching models are still only trained on a few mid-sized datasets. In this paper, we revisit local feature matching from a data-driven perspective. In our approach, which we call LoMa, we combine large and diverse data mixtures, modern training recipes, scaled model capacity, and scaled compute, resulting in remarkable gains in performance. Since current standard benchmarks mainly rely on collecting sparse views from successful 3D reconstructions, the evaluation of progress in feature matching has been limited to relatively easy image pairs. To address the resulting saturation of benchmarks, we collect 1000 highly challenging image pairs from internet data into a new dataset called HardMatch. Ground truth correspondences for HardMatch are obtained via manual annotation by the authors. In our extensive benchmarking suite, we find that LoMa makes outstanding progress across the board, outperforming the state-of-the-art method ALIKED+LightGlue by +18.6 mAA on HardMatch, +29.5 mAA on WxBS, +21.4 (1m, 10^circ) on InLoc, +24.2 AUC on RUBIK, and +12.4 mAA on IMC 2022. We release our code and models publicly at https://github.com/davnords/LoMa.

  • 9 authors
·
Apr 5

Unified Map Prior Encoder for Mapping and Planning

Online mapping and end-to-end (E2E) planning in autonomous driving remain largely sensor-centric, leaving rich map priors, including HD/SD vector maps, rasterized SD maps, and satellite imagery, underused because of heterogeneity, pose drift, and inconsistent availability at test time. We present UMPE, a Unified Map Prior Encoder that can ingest any subset of four priors and fuse them with BEV features for both mapping and planning. UMPE has two branches. The vector encoder pre-aligns HD/SD polylines with a frame-wise SE(2) correction, encodes points via multi-frequency sinusoidal features, and produces polyline tokens with confidence scores. BEV queries then apply cross-attention with confidence bias, followed by normalized channel-wise gating to avoid length imbalance and softly down-weight uncertain sources. The raster encoder shares a ResNet-18 backbone conditioned by FiLM with scaling and shift at every stage, performs SE(2) micro-alignment, and injects priors through zero-initialized residual fusion, so the network starts from a do-no-harm baseline and learns to add only useful prior evidence. A vector-then-raster fusion order reflects the inductive bias of geometry first, appearance second. On nuScenes mapping, UMPE lifts MapTRv2 from 61.5 to 67.4 mAP (+5.9) and MapQR from 66.4 to 71.7 mAP (+5.3). On Argoverse2, UMPE adds +4.1 mAP over strong baselines. UMPE is compositional: when trained with all priors, it outperforms single-prior models even when only one prior is available at test time, demonstrating powerset robustness. For E2E planning with the VAD backbone on nuScenes, UMPE reduces trajectory error from 0.72 to 0.42 m L2 on average (-0.30 m) and collision rate from 0.22% to 0.12% (-0.10%), surpassing recent prior-injection methods. These results show that a unified, alignment-aware treatment of heterogeneous map priors yields better mapping and better planning.

  • 15 authors
·
May 3

Neural Scene Flow Prior

Before the deep learning revolution, many perception algorithms were based on runtime optimization in conjunction with a strong prior/regularization penalty. A prime example of this in computer vision is optical and scene flow. Supervised learning has largely displaced the need for explicit regularization. Instead, they rely on large amounts of labeled data to capture prior statistics, which are not always readily available for many problems. Although optimization is employed to learn the neural network, the weights of this network are frozen at runtime. As a result, these learning solutions are domain-specific and do not generalize well to other statistically different scenarios. This paper revisits the scene flow problem that relies predominantly on runtime optimization and strong regularization. A central innovation here is the inclusion of a neural scene flow prior, which uses the architecture of neural networks as a new type of implicit regularizer. Unlike learning-based scene flow methods, optimization occurs at runtime, and our approach needs no offline datasets -- making it ideal for deployment in new environments such as autonomous driving. We show that an architecture based exclusively on multilayer perceptrons (MLPs) can be used as a scene flow prior. Our method attains competitive -- if not better -- results on scene flow benchmarks. Also, our neural prior's implicit and continuous scene flow representation allows us to estimate dense long-term correspondences across a sequence of point clouds. The dense motion information is represented by scene flow fields where points can be propagated through time by integrating motion vectors. We demonstrate such a capability by accumulating a sequence of lidar point clouds.

  • 3 authors
·
Nov 1, 2021

GeoDream: Disentangling 2D and Geometric Priors for High-Fidelity and Consistent 3D Generation

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

  • 6 authors
·
Nov 29, 2023 1

A theory of representation learning gives a deep generalisation of kernel methods

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

  • 6 authors
·
Aug 30, 2021

LTGS: Long-Term Gaussian Scene Chronology From Sparse View Updates

Recent advances in novel-view synthesis can create the photo-realistic visualization of real-world environments from conventional camera captures. However, acquiring everyday environments from casual captures faces challenges due to frequent scene changes, which require dense observations both spatially and temporally. We propose long-term Gaussian scene chronology from sparse-view updates, coined LTGS, an efficient scene representation that can embrace everyday changes from highly under-constrained casual captures. Given an incomplete and unstructured Gaussian splatting representation obtained from an initial set of input images, we robustly model the long-term chronology of the scene despite abrupt movements and subtle environmental variations. We construct objects as template Gaussians, which serve as structural, reusable priors for shared object tracks. Then, the object templates undergo a further refinement pipeline that modulates the priors to adapt to temporally varying environments based on few-shot observations. Once trained, our framework is generalizable across multiple time steps through simple transformations, significantly enhancing the scalability for a temporal evolution of 3D environments. As existing datasets do not explicitly represent the long-term real-world changes with a sparse capture setup, we collect real-world datasets to evaluate the practicality of our pipeline. Experiments demonstrate that our framework achieves superior reconstruction quality compared to other baselines while enabling fast and light-weight updates.

  • 4 authors
·
Oct 10, 2025

A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence

Text-to-image diffusion models have made significant advances in generating and editing high-quality images. As a result, numerous approaches have explored the ability of diffusion model features to understand and process single images for downstream tasks, e.g., classification, semantic segmentation, and stylization. However, significantly less is known about what these features reveal across multiple, different images and objects. In this work, we exploit Stable Diffusion (SD) features for semantic and dense correspondence and discover that with simple post-processing, SD features can perform quantitatively similar to SOTA representations. Interestingly, the qualitative analysis reveals that SD features have very different properties compared to existing representation learning features, such as the recently released DINOv2: while DINOv2 provides sparse but accurate matches, SD features provide high-quality spatial information but sometimes inaccurate semantic matches. We demonstrate that a simple fusion of these two features works surprisingly well, and a zero-shot evaluation using nearest neighbors on these fused features provides a significant performance gain over state-of-the-art methods on benchmark datasets, e.g., SPair-71k, PF-Pascal, and TSS. We also show that these correspondences can enable interesting applications such as instance swapping in two images.

  • 7 authors
·
May 24, 2023

LiftImage3D: Lifting Any Single Image to 3D Gaussians with Video Generation Priors

Single-image 3D reconstruction remains a fundamental challenge in computer vision due to inherent geometric ambiguities and limited viewpoint information. Recent advances in Latent Video Diffusion Models (LVDMs) offer promising 3D priors learned from large-scale video data. However, leveraging these priors effectively faces three key challenges: (1) degradation in quality across large camera motions, (2) difficulties in achieving precise camera control, and (3) geometric distortions inherent to the diffusion process that damage 3D consistency. We address these challenges by proposing LiftImage3D, a framework that effectively releases LVDMs' generative priors while ensuring 3D consistency. Specifically, we design an articulated trajectory strategy to generate video frames, which decomposes video sequences with large camera motions into ones with controllable small motions. Then we use robust neural matching models, i.e. MASt3R, to calibrate the camera poses of generated frames and produce corresponding point clouds. Finally, we propose a distortion-aware 3D Gaussian splatting representation, which can learn independent distortions between frames and output undistorted canonical Gaussians. Extensive experiments demonstrate that LiftImage3D achieves state-of-the-art performance on two challenging datasets, i.e. LLFF, DL3DV, and Tanks and Temples, and generalizes well to diverse in-the-wild images, from cartoon illustrations to complex real-world scenes.

  • 9 authors
·
Dec 12, 2024

Likelihood Training of Cascaded Diffusion Models via Hierarchical Volume-preserving Maps

Cascaded models are multi-scale generative models with a marked capacity for producing perceptually impressive samples at high resolutions. In this work, we show that they can also be excellent likelihood models, so long as we overcome a fundamental difficulty with probabilistic multi-scale models: the intractability of the likelihood function. Chiefly, in cascaded models each intermediary scale introduces extraneous variables that cannot be tractably marginalized out for likelihood evaluation. This issue vanishes by modeling the diffusion process on latent spaces induced by a class of transformations we call hierarchical volume-preserving maps, which decompose spatially structured data in a hierarchical fashion without introducing local distortions in the latent space. We demonstrate that two such maps are well-known in the literature for multiscale modeling: Laplacian pyramids and wavelet transforms. Not only do such reparameterizations allow the likelihood function to be directly expressed as a joint likelihood over the scales, we show that the Laplacian pyramid and wavelet transform also produces significant improvements to the state-of-the-art on a selection of benchmarks in likelihood modeling, including density estimation, lossless compression, and out-of-distribution detection. Investigating the theoretical basis of our empirical gains we uncover deep connections to score matching under the Earth Mover's Distance (EMD), which is a well-known surrogate for perceptual similarity. Code can be found at https://github.com/lihenryhfl/pcdm{this https url}.

  • 3 authors
·
Jan 12, 2025