Cycle Consistency

We study the recovery of forward and reverse quadratic optimal-transport maps from unpaired samples in high dimensions. We introduce a bidirectional neural framework in which the learned maps induce forward and backward displacement interpolants, while the training objective combines bidirectional quadratic action, discriminator-restricted Jensen-Shannon endpoint objectives, and two-sided cycle consistency. The construction requires neither precomputed sample pairings nor an explicit convex-potential parameterization. For absolutely continuous probability measures supported on a compact convex set, and under the stated generator-approximation, discriminator-richness, and minimizer-attainment conditions, we prove a population recovery theorem: for every prescribed accuracy, the sum of the corresponding $L^2$ errors between any global minimizer and the forward and reverse quadratic Brenier maps is below that accuracy, provided the discriminator level is sufficiently large and the annealing action weight becomes sufficiently small. Moreover, the cycle loss is bounded above by $λW_2^2(μ_0,μ_1)$. Complementary results quantify approximate invertibility and show that exact endpoint Jensen-Shannon divergence and cycle consistency control missing target mass and many-to-one map collapse, respectively. Experiments on Swiss roll, MNIST, CelebA, single-cell perturbation data, and chest X-ray images evaluate endpoint fidelity, transport cost, inverse consistency, and the geometry of the induced interpolations.

Object 6D pose estimation formulations have progressively reduced reliance on object-specific priors, evolving from explicit 3D models to multi-view object captures to single reference images. We take this progression to its extreme by introducing prior-free relative 6D pose estimation, which lifts the assumption of knowing which object is to be posed within the scene. This novel setting aims to estimate the relative poses of multiple instances of an unknown object within the same image, without requiring CAD models, templates, or reference images. We solve this by formulating a novel method (PROSE) that finds coarse correspondences between object instances using multimodal foundation features, thus requiring no training. We refine these correspondences by imposing cycle consistency across tuples of instances, and leverage the resulting globally consistent correspondences to estimate the relative 6D pose between any pair of instances. To enable systematic evaluation, we design a novel benchmark (PRENCH) built from three multi-instance BOP datasets and enriched with task-specific metadata. PROSE consistently outperforms baselines obtained by adapting state-of-the-art single-image methods to the proposed setting, while requiring neither task-specific supervision nor additional learned components. Project website: https://tev-fbk.github.io/PROSE/

Bidirectional unpaired image translation must preserve source-specific structure while learning coherent transformations in both directions without paired supervision. Existing methods typically employ two direction-specific generators or train separate one-way models. Even when linked by cycle consistency, such models constrain only the round-trip endpoint reconstruction, without requiring the two directions to obey a common local transformation rule. We propose UniCycleFlow, a rectified-flow framework that represents bidirectional translation as forward and reverse integration of a single time-conditioned velocity field. This formulation organizes both directions within the same continuous dynamics, rather than coupling otherwise separate endpoint mappings. A key challenge is that unpaired data provide no meaningful source--target coupling from which rectified-flow trajectories can be constructed. UniCycleFlow addresses this challenge by learning deterministic source-conditioned endpoints whose marginal distributions are adversarially matched to the opposite domains. The resulting paths are regularized by stop-gradient self-flow matching for intermediate velocity supervision, discrete cycle closure for forward--reverse consistency, and representation path-velocity regularization for controlling localized feature changes along the trajectory. Across ten translation directions, UniCycleFlow achieves the lowest FID on 7 of 10 tasks using a single Euler evaluation and obtains the best average FID of 55.1.

Decision-time planning with action-conditioned world models has become a popular paradigm for embodied control. However, the standard planning cost judges a candidate solely by how close its predicted terminal state lies to the goal, leaving the realizability of the intermediate transitions unchecked--a predicted trajectory can look convincing while the environment rollout drifts away from it. In this paper, we propose ACID, a decision-time planning framework that introduces cycle action consistency: the action inferred backward from a predicted transition by an inverse dynamics model should recover the one that was conditioned on. We fold this per-step residual into the planning cost via a scale-invariant adaptive weight. Across four action-conditioned world models and eight tasks encompassing object manipulation and articulated control in simulation, visual navigation, and real-robot manipulation, ACID consistently improves planning and matches the baseline's accuracy with substantially less planning compute.

We propose triangular consistency as a first-principled constraint for optical flow, which is agnostic to network architecture, supervision type, and dataset, and applies to both image-pair and multi-frame settings. This simple but powerful constraint is to compose two flows to induce a third flow and enforce consistency among the three. The composed flows may arise from (i) image pairs, yielding cycle consistency; (ii) multiple video frames, producing longer-range motion through temporal chaining; or (iii) image pairs combined with controlled synthetic transformations, which becomes data augmentation. This triangular consistency introduces negligible computational overhead and requires no additional annotations. Since it is derived directly from the geometry of optical flow, it does not rely on model-specific assumptions and serves as a ``universal'' plug-and-play component for optical flow training. Experiments show consistent improvement across supervised, unsupervised, and transfer learning settings.

Modern generative models possess a deep understanding of visual content, yet training them for image editing typically requires massive datasets of paired examples. This limits scalability, especially for video editing where collecting paired data is prohibitively expensive. We propose Bootstrap Your Generator (ByG), a general framework for unpaired training of flow matching editing models. It leverages the base model's knowledge without any external signal. Our approach pairs instruction-following cues extracted from the frozen model with cycle-consistency for structure preservation. To make this tractable, we propose to route gradients from downstream losses over clean predictions to noisy training states. We demonstrate state-of-the-art results on challenging data-scarce image and video editing scenarios. Extensive evaluations and user studies show that our method effectively generalizes to unseen domains and outperforms supervised baselines trained on millions of samples. Analysis reveals that our gradient routing bridges the train-inference gap, and extracting semantic cues from a base model provides a robust training signal that obviates the need for external reward models.

Self-supervised video Object-Centric Learning (OCL) aims to discover distinct objects and associate them across time, whereas self-supervised Multi-Object Tracking (MOT) focuses on associating pre-defined object detections or segmentations. Although well-established in MOT, Cycle Consistency (CC) cannot naively or explicitly apply to the latent slot space of OCL. Unlike the deterministic and ideal object representations in MOT, OCL slots are inherently stochastic and ambiguous due to non-unique scene decompositions. Enforcing explicit cycle consistency (ECC) on slots imposes rigid mean seeking. This severely penalizes the model for exploring alternative but equally valid decompositions, thereby driving towards feature collapse. To resolve this dilemma, we propose Implicit Cycle Consistency (ICC), which shifts the cycle-consistency constraint from the restrictive slot space to the continuous reconstruction manifold, encouraging slots to reach a soft consensus on collectively interpreting the visual scene rather than forcing rigid point-to-point feature alignment. Extensive experiments on complex video OCL benchmarks demonstrate that ICC avoids feature collapse and outperforms ECC baselines. Our source code, model checkpoints and training logs are provided on https://github.com/Genera1Z/ICC.

Autoformalization - automatically translating natural language mathematical texts into formal proof language such as Lean4 - can help accelerate AI-assisted mathematical research, be it via proof verification or proof search. I fine-tune Qwen3.5-2B with LoRA for natural language to Lean4 formalization on FineLeanCorpus and consider three training regimes: supervised fine-tuning (SFT) with curriculum learning (difficulty 1 to 10), SFT without curriculum ordering, and reinforcement learning using group relative policy optimization (GRPO) with a cycle consistency reward. Cycle consistency measures how well the meaning of a statement is preserved through a NL to Lean4 to NL' loop, computed as cosine similarity of off-the-shelf sentence embeddings. On an unseen subset of FineLeanCorpus (FLC) and on PutnamBench, RL substantially outperforms both SFT variants (mean cycle consistency 0.669 vs. 0.513 on FLC; 0.561 vs. 0.422 on PutnamBench), while increasing cross-entropy loss by only 0.011 nats, with minimal impact on formalization quality. Curriculum ordering provides no measurable benefit over shuffled training.

Visual-Language Models (VLMs) have achieved remarkable progress in image captioning, visual question answering, and visual reasoning. Yet they remain prone to vision-language misalignment, often producing overly generic or hallucinated descriptions. Existing approaches address this via instruction tuning-requiring costly, large-scale annotated datasets or via complex test-time frameworks for caption refinement. In this work, we revisit image-text alignment through the lens of cycle consistency: given an image and a caption generated by an image-to-text model, the backward mapping through a text-to-image model should reconstruct an image that closely matches the original. In our setup, a VLM serves as the image-to-text component, while a pre-trained text-to-image model closes the loop by reconstructing the image from the generated caption. Building on this, we introduce CycleCap, a fine-tuning scheme to improve image captioning using Group Relative Policy Optimization (GRPO) with a reward based on the similarity between the original and reconstructed images, computed on-the-fly. Unlike previous work that uses cycle consistency loss for preference dataset construction, our method leverages cycle consistency directly as a self-supervised training signal. This enables the use of raw images alone, eliminating the need for curated image-text datasets, while steering the VLM to produce more accurate and grounded text descriptions. Applied to four VLMs ranging from 1B to 7B parameters, CycleCap yields consistent improvements across captioning and hallucination benchmarks, surpassing state-of-the-art methods that rely on supervised cycle consistency training.

In this paper, we introduce a consistency-driven dual LSTM framework for accurately learning both the forward and inverse kinematics of a pneumatically actuated soft robotic arm integrated into a wearable device. This approach effectively captures the nonlinear and hysteretic behaviors of soft pneumatic actuators while addressing the one-to-many mapping challenge between actuation inputs and end-effector positions. By incorporating a cycle consistency loss, we enhance physical realism and improve the stability of inverse predictions. Extensive experiments-including trajectory tracking, ablation studies, and wearable demonstrations-confirm the effectiveness of our method. Results indicate that the inclusion of the consistency loss significantly boosts prediction accuracy and promotes physical consistency over conventional approaches. Moreover, the wearable soft robotic arm demonstrates strong human-robot collaboration capabilities and adaptability in everyday tasks such as object handover, obstacle-aware pick-and-place, and drawer operation. This work underscores the promising potential of learning-based kinematic models for human-centric, wearable robotic systems.

Cross-Domain Few-Shot Learning (CDFSL) adapts models trained with large-scale general data (source domain) to downstream target domains with only scarce training data, where the research on vision-language models (e.g., CLIP) is still in the early stages. Typical downstream domains, such as medical diagnosis, require fine-grained visual cues for interpretable recognition, but we find that current fine-tuned CLIP models can hardly focus on these cues, albeit they can roughly focus on important regions in source domains. Although current works have demonstrated CLIP's shortcomings in capturing local subtle patterns, in this paper, we find that the domain gap and scarce training data further exacerbate such shortcomings, much more than that of holistic patterns, which we call the local misalignment problem in CLIP-based CDFSL. To address this problem, due to the lack of supervision in aligning local visual features and text semantics, we turn to self-supervision information. Inspired by the translation task, we propose the CC-CDFSL method with cycle consistency, which translates local visual features into text features and then translates them back into visual features (and vice versa), and constrains the original features close to the translated back features. To reduce the noise imported by richer information in the visual modality, we further propose a Semantic Anchor mechanism, which first augments visual features to provide a larger corpus for the text-to-image mapping, and then shrinks the image features to filter out irrelevant image-to-text mapping. Extensive experiments on various benchmarks, backbones, and fine-tuning methods show we can (1) effectively improve the local vision-language alignment, (2) enhance the interpretability of learned patterns and model decisions by visualizing patches, and (3) achieve state-of-the-art performance.

Transforming image features from perspective view (PV) space to bird's-eye-view (BEV) space remains challenging in autonomous driving due to depth ambiguity and occlusion. Although several view transformation (VT) paradigms have been proposed, the challenge still remains. In this paper, we propose a new regularization framework, dubbed CycleBEV, that enhances existing VT models for BEV semantic segmentation. Inspired by cycle consistency, widely used in image distribution modeling, we devise an inverse view transformation (IVT) network that maps BEV segmentation maps back to PV segmentation maps and use it to regularize VT networks during training through cycle consistency losses, enabling them to capture richer semantic and geometric information from input PV images. To further exploit the capacity of the IVT network, we introduce two novel ideas that extend cycle consistency into geometric and representation spaces. We evaluate CycleBEV on four representative VT models covering three major paradigms using the large-scale nuScenes dataset. Experimental results show consistent improvements -- with gains of up to 0.74, 4.86, and 3.74 mIoU for drivable area, vehicle, and pedestrian classes, respectively -- without increasing inference complexity, since the IVT network is used only during training. The implementation code is available at https://github.com/JeongbinHong/CycleBEV.

Transferring visual style between images while preserving semantic correspondence between similar objects remains a central challenge in computer vision. While existing methods have made great strides, most of them operate at global level but overlook region-wise and even pixel-wise semantic correspondence. To address this, we propose CoCoDiff, a novel training-free and low-cost style transfer framework that leverages pretrained latent diffusion models to achieve fine-grained, semantically consistent stylization. We identify that correspondence cues within generative diffusion models are under-explored and that content consistency across semantically matched regions is often neglected. CoCoDiff introduces a pixel-wise semantic correspondence module that mines intermediate diffusion features to construct a dense alignment map between content and style images. Furthermore, a cycle-consistency module then enforces structural and perceptual alignment across iterations, yielding object and region level stylization that preserves geometry and detail. Despite requiring no additional training or supervision, CoCoDiff delivers state-of-the-art visual quality and strong quantitative results, outperforming methods that rely on extra training or annotations.