Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching. Along the way, the underlying techniques have become more complicated and various beliefs about what drives strong empirical performance have taken hold. Due to the success of diffusion models and flow matching, one of the more common beliefs is the importance of transforming the noise distribution to the data distribution gradually through many small transformations. We ask whether this is truly necessary, and take a minimalist approach to designing a competitive generative model. We start with the bare-bones essentials, namely just a training objective and a model. We purposefully make both simple. For the training objective, we choose Implicit Maximum Likelihood Estimation (IMLE), and eschew more complicated alternatives such as variational inference, adversarial training and numerical integration. For the model, we eschew transformers and instead choose a moderately sized convolutional network. Then we judiciously added elements that are truly essential, which surprisingly do not include iterative denoising. The result is a single-step parameter-efficient generative model that produces high quality samples at fast speed: it achieves an FID of 2.56 on ImageNet 256 and simultaneously attains good precision and recall.
https://arxiv.org/abs/2607.19332
Whole-slide image (WSI) diagnosis requires identifying diagnostically relevant regions, examining them across magnifications, and integrating multi-scale evidence. However, most existing pathology benchmarks evaluate models on pre-cropped patches or pre-extracted slide features, leaving their ability to acquire evidence directly from gigapixel WSIs largely untested. We introduce PathAgentBench, a benchmark for evaluating evidence-seeking vision-language models (VLMs) across four complementary capabilities: image-to-text matching for evidence interpretation, text-to-image retrieval for evidence verification, diagnostic-region localization for evidence acquisition, and multi-scale reasoning for evidence integration. The benchmark is organized as a diagnostic tree that links nested regions across magnifications with scale-specific findings and path-level diagnoses. It contains 1,822 TCGA WSIs and 17,135 diagnostic paths annotated by ten board-certified pathologists. An additional private cohort of 190 breast cancer WSIs with detailed annotations is used to evaluate autonomous whole-slide exploration. We evaluate 20 general-purpose, medical, and pathology-specialized models. Leading open-weight models achieve over 93% accuracy in multi-scale reasoning and over 50% accuracy in both cross-modal matching tasks. In contrast, diagnostic-region localization remains challenging: the best text-guided mean intersection-over-union is below 0.09, underperforming a simple center-based heuristic. During autonomous exploration, the unconditional hit rate decreases from 0.522 at low magnification to 0.185 at intermediate magnification and 0.020 at high magnification. These results reveal a pronounced gap between reasoning over curated evidence and acquiring that evidence directly from WSIs. PathAgentBench provides a unified framework for measuring and improving evidence-seeking pathology models.
https://arxiv.org/abs/2607.19261
Inferring contrast enhancement from one pre-contrast breast MRI slice is underdetermined: post-contrast appearance contains physiological information that is not uniquely encoded in baseline anatomy. Optimizing only paired pixel fidelity can suppress uncertain lesion enhancement, whereas adversarial or stochastic generative objectives can favor realistic post-contrast appearance without guaranteeing patient-specific lesion fidelity. We introduce MIRAGE, a residual 2D U-Net that combines global reconstruction and perceptual losses with three forms of lesion-aware supervision available only during training: an asymmetric penalty for missed tumor enhancement, multi-scale auxiliary tumor segmentation, and guidance through a frozen post-contrast tumor segmentation nnU-Net. We evaluate the method on 301 cases from the multi-centre MAMA-SYNTH data using eight complementary image-, region-, radiomics-, and segmentation-based metrics. MIRAGE ranks first on six metrics and markedly improves downstream lesion localization over tuned pix2pix, conditional diffusion, and latent bridge-matching baselines. The generative alternatives retain advantages in LPIPS or contrast classification, revealing a clear fidelity-utility trade-off. Leave-one-in and leave-one-out ablations show that the losses are partly redundant for lesion localization but exert distinct effects on appearance, radiomics, and boundary accuracy. These results support task-aware synthesis while also showing that its apparent optimality is conditional on the downstream models and metrics used to define utility.
https://arxiv.org/abs/2607.19137
Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K, ScanNet++ and ETH3D, our method achieves strong performance against recent scene generation baselines in both per-view appearance and aggregated 3D geometry, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation. The project page can be found $\href{this https URL}{\text{here}}$.
https://arxiv.org/abs/2607.19120
Edit-conditioned 3D scene retrieval pairs a reference 3D room with a natural-language modification and retrieves rooms from a corpus that satisfy the edit. Three lines of prior work each fall short on this task. 2D composed image retrieval reasons over pixel-level edits and has no primitive for 3D object sets. 3D foundation encoders embed individual objects but cannot compose at the scene level. 3D scene-grounding methods localize references inside a static scene rather than rank modified rooms across a corpus. We present CR-Refiner, a training-free reranker that wraps any base retriever's top-K candidates with three components. A frozen LLM parses the edit into a structured query entity, and each candidate is scored by an unbalanced optimal-transport problem over a 1xG cost matrix coupling category, style, material, and geometry. The unbalanced solver lets the single-entity query drop mass on irrelevant objects, modelling the asymmetry directly. An axis-conditional structural prior adds size-keyword cues for geometric edits and subject-anchor direction cues for spatial edits. An LLM verifier refines the top three candidates with continuous confidence. Because no benchmark evaluates compositional matching over 3D object sets, we additionally release 3D-CER, 4,963 edit-conditioned queries over a 23,381-room indoor corpus across five edit axes, with multi-positive ground truth, CIRR-style hard subsets, and zero-target adversarials. Across three qualitatively distinct base retrievers, CR-Refiner consistently improves hard-subset R@1 and mAP@10 on every edit axis.
https://arxiv.org/abs/2607.19115
Large-scale visual generators are increasingly capable but costly to train, fine-tune, and deploy. We introduce Mage-Flow, a compact 4B-scale generative stack for efficient text-to-image generation and instruction-based image editing. The stack is built from two co-designed components: Mage-VAE, a lightweight high-fidelity latent tokenizer, and a Native-Resolution Multimodal Diffusion Transformer trained with rectified flow matching. Mage-VAE uses one-step diffusion-style encoding and decoding with anchor-latent regularization, preserving the reconstruction quality of strong public VAEs while reducing tokenization cost by more than an order of magnitude. Together with native-resolution packing and stack-level CUDA kernel fusion, the stack supports flexible-resolution training and improves end-to-end training throughput by about $2.5\times$. Built on this foundation, we develop a complete model family with Base, RL-aligned, and Turbo variants for both generation and editing. Diffusion-NFT improves prompt following, text rendering, aesthetic quality, and editing fidelity, while few-step distillation with adversarial perceptual guidance produces 4-step Turbo models for low-latency inference. Despite its compact scale, Mage-Flow and Mage-Flow-Edit achieves competitive performance across standard generation and editing benchmarks. More importantly, the Turbo variants make high-resolution generation and editing practical for interactive use: at $1024^2$ resolution on a single NVIDIA A100 GPU, Mage-Flow-Turbo generates an image in 0.59s, and Mage-Flow-Edit-Turbo edits an image in 1.02s, while maintaining a small memory footprint. These results show that careful tokenizer--backbone--system co-design can deliver strong high-resolution generation and editing within an efficient 4B model family.
https://arxiv.org/abs/2607.19064
On-policy Distillation (OPD) supervises a student model on trajectories sampled from its own policy by minimizing the divergence between the output distributions of the teacher and student at each token position, thereby providing dense token-level supervision. Although existing OPD methods have demonstrated strong performance in improving the reasoning ability of student models, their objectives fundamentally rely on token-level distribution matching. Consequently, they lack an explicit signal for comparing a token's relative compatibility across reasoning modes and thus do not directly model preferences between these modes. To address this limitation, we propose COPD, a contrastive OPD framework. Specifically, for each token generated by the student model, a frozen teacher model scores the same student state under two contrasting instructions that elicit light and heavy reasoning. The difference between the resulting log probabilities serves as a token-level advantage signal to guide the OPD update. Rather than merely imitating a single teacher distribution, COPD directly encourages the student model to learn more concise and efficient reasoning strategies. We conduct experiments on nine multimodal benchmarks covering both reasoning and understanding tasks. The results show that COPD substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales. Furthermore, the contrastive formulation can be seamlessly integrated into the On-policy Self-distillation (OPSD) framework, where self-contrastive supervision is constructed without an additional teacher model, thereby enabling the model to distill itself toward lightweight reasoning.
https://arxiv.org/abs/2607.19046
Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models on tasks such as mathematical reasoning and code generation. However, most RLVR methods assign a scalar outcome reward to an entire trajectory, resulting in sparse supervision and limited token-level credit assignment. On-policy distillation (OPD) provides denser supervision by distilling token-level distributions from a stronger teacher model, but requires an additional teacher and typically assumes a shared vocabulary. On-policy self-distillation (OPSD) removes this dependency by conditioning the same model on privileged information to construct a teacher policy. However, directly matching the teacher distribution may cause information leakage and unstable optimization. RLSD avoids direct matching by using the teacher signal only to modulate update magnitudes, but it cannot provide an explicit correction direction when the sampled reasoning fails. To address this tradeoff, we introduce $\mathrm{H}^{2}\mathrm{SD}$, a hybrid hindsight self distillation framework that uses the teacher differently according to trajectory correctness. For successful trajectories, the teacher receives the student response confirmed as correct together with a rephrasing instruction, and its probabilities on the original response tokens are used to modulate update magnitudes without changing the direction determined by the reward. For failed trajectories, we condition the teacher on a reference hint containing key reasoning steps and a verified answer, and minimize the reverse KL divergence from the student to the teacher. Experiments on multiple challenging reasoning benchmarks show that H$^2$SD consistently outperforms representative RLVR, OPSD, and RLSD baselines while maintaining stable optimization and favorable generation efficiency.
https://arxiv.org/abs/2607.18955
We present NGPS (Next-Generation Positioning System), a visual geo-localization framework for high-altitude UAVs that provides GPS-free absolute positioning by matching down-facing images to georeferenced satellite imagery with deep features. The system combines (1) adaptive confidence-weighted UKF fusion, where NGPS covariance is modulated by RANSAC inlier ratio, reprojection error, and match confidence; (2) velocity-predictive kernel extraction, using VIO velocity to predict the satellite search region; and (3) an asynchronous multi-rate temporal priority queue that interleaves absolute position (1-2 Hz), VIO (10-20 Hz), and IMU (100-200 Hz) updates in chronological order. Globally optimized poses from VINS pose-graph optimization, anchored by NGPS corrections, further enable real-time 2.5D georeferenced orthomosaic reconstruction. On five flight sequences (60-150 m AGL), NGPS achieves 2.94 m position RMSE, with worst-case ATE 6.04 m at 150 m AGL and 2 m/s, yielding a 3.5x improvement over standalone monocular VIO. The system runs in real time on an NVIDIA Jetson Orin NX. Part of the implementation is open-sourced at this https URL.
https://arxiv.org/abs/2607.18936
Instance-level artwork recognition requires matching a handheld visitor photograph to a specific work in a large museum collection. This is challenging because painting datasets typically provide clean catalog images for training, while test queries are captured under oblique viewpoints, gallery lighting, reflections, frames, and other scene-level variations. We present SynGallery, a synthetic gallery dataset for artwork retrieval that addresses this gap without collecting additional real photographs. Starting from catalog images of real paintings, we place each artwork into a procedurally generated 3D gallery scene and render it from multiple viewpoints under varied geometric and appearance conditions, while preserving the exact identity of the original work. The resulting dataset contains 24,490 rendered views of 4,898 paintings from the Met benchmark. We show that these synthetic views provide a stronger training signal than the corresponding studio photographs. At the same number of training data points, training only on SynGallery improves art painting recognition from 67.18 to 73.47 GAP$^-$. When added to the full Met training set, SynGallery improves the published benchmark protocol from 35.97 to 38.48 GAP. Ablation experiments show that the gain comes primarily from geometric viewpoint variation rather than photographic realism: blur, sensor noise, and image compression consistently reduce performance.
https://arxiv.org/abs/2607.18907
Accurate skin lesion classification can benefit from lesion segmentation masks, but requiring masks or an auxiliary segmentation model during inference reduces clinical practicality and increases computational complexity. This work introduces Privileged Lesion-Context Relational Distillation (PLCRD), a teacher-student framework that exploits lesion masks exclusively during training while preserving image-only inference. The privileged teacher jointly analyzes the original dermoscopic image and its mask-guided lesion region to learn lesion-specific and contextual diagnostic representations. An image-only student is then trained through complementary knowledge-transfer mechanisms that convey the teacher's diagnostic distribution, lesion-focused attention, inter-lesion relational geometry, and lesion-context structure. PLCRD decomposes deep representations into lesion and contextual embeddings and transfers their relational organization through inter-lesion similarity alignment, lesion-context affinity matching, separation regularization, and class-aware relational learning. This formulation avoids direct feature matching between heterogeneous teacher and student architectures and enables the student to internalize mask-informed diagnostic structure without accessing masks at deployment. The framework was evaluated on HAM10000 using lesion-disjoint data partitioning and externally validated on ISIC 2018 without retraining. PLCRD achieved a lesion-level macro-F1 of 0.773 +/- 0.018, balanced accuracy of 0.764 +/- 0.023, and macro-AUROC of 0.976 +/- 0.002 on HAM10000, together with a macro-F1 of 0.732 +/- 0.008 on ISIC 2018. The results indicate that privileged lesion annotations can be transformed into transferable relational knowledge, yielding a practical and interpretable approach to mask-free skin lesion classification.
https://arxiv.org/abs/2607.18773
Magnetic resonance imaging comes in various modality contrasts that provide complementary anatomical and pathological information. Complete multimodal acquisitions are often unavailable due to time and protocol constraints. This leads to real-world datasets with missing modalities, where conventional medical image translation methods are typically limited to fixed source-target settings or require retraining for each observed source-target pair. We propose a unified framework that formulates missing-modality generation as a linear inverse problem under a joint distribution and solves it via posterior sampling with a flow matching model. By learning a joint prior over the complete modality set, our method can reconstruct arbitrary missing modalities at inference time by guiding the sampling trajectory to enforce measurement consistency with observed modalities. We further mitigate inter-modality error propagation in multi-target generation by adopting a many-to-one sampling strategy. Experiments on BraTS and IXI datasets show that our method achieves the best performance over baselines across most missing-modality scenarios. In downstream tumor segmentation, synthesized images from our method result in higher segmentation performance, indicating better preservation of clinically relevant structures.
https://arxiv.org/abs/2607.18763
Understanding the computational basis of action recognition is a central challenge in social cognition as well as in human-robot interaction. Inspired by the Mirror Neuron System (MNS), we propose a two-level architecture for motor primitive discovery and online phase recognition applied to the NICO humanoid robot. At the first level, two Self-Organising Maps (SOMs) learn topographic representations of arm kinematics (A-SOM) and hand kinematics (H-SOM) from simulated trials covering seven motor actions. The maps are trained on non-redundant features identified through hierarchical correlation analysis of motion trajectories. The results show that the two SOMs encode complementary aspects of motor behaviour. At the second level, an Echo State Network (ESN) evaluates whether temporal trajectories of SOM activations, represented by consecutive best-matching units, are sufficient for online recognition of the currently executed movement phase. The results show that SOM-based trajectories preserve the dominant phase-discriminative structure of the movement, while contextual information provides only a secondary refinement. Our contribution is the integration of established SOM and ESN methods within an MNS-inspired architecture for motor primitive representation and online phase recognition. The results are compatible with the computational hypothesis that self-organised motor representations, when temporally integrated, can support accurate online recognition of ongoing movement phases.
https://arxiv.org/abs/2607.18737
Video multimodal large language models have shown strong capability in video understanding, yet their adaptation to sequentially evolving domains remains underexplored. In real-world deployments, video data often arrives continuously from heterogeneous domains, requiring the model to acquire new domain-specific knowledge without overwriting previously learned capabilities. Existing continual learning methods typically rely on shared adaptation spaces, which can induce severe cross-domain interference and catastrophic forgetting. We propose Distribution-Aware Expert Routing, a parameter-efficient framework for continual Video-MLLM adaptation over evolving domains. DAER maintains domain-isolated lightweight experts while keeping the pretrained Video-MLLM backbone frozen, thereby decoupling domain-specific adaptation from the general multimodal knowledge of the pretrained model. To enable fine-grained specialization, we introduce an intra-domain distribution-aware routing mechanism that matches each input to expert-level prototype reservoirs using MMD. To address the absence of task identities at inference time, we further propose an inter-domain routing mechanism that performs prototype matching in a discriminative subspace for robust domain identification. In addition, we introduce adaptive domain merging to improve parameter scalability and adopt a two-stage optimization strategy to stabilize expert specialization during continual learning. We evaluate DAER by curating a domain-incremental benchmark built from ten VidQA datasets covering diverse visual environments and reasoning demands. Experiments on two strong Video-MLLM backbones show that DAER consistently outperforms prior methods.
https://arxiv.org/abs/2607.18716
Visible-Infrared Person Re-Identification (VI-ReID) operates under a closed-world assumption, where queries and galleries are from heterogeneous modalities. However, in open-world scenarios, both sets are likely to contain homogeneous and heterogeneous modality images. A query may consist of visible-only, infrared-only, or mixed-modality images, while galleries present multi-modal images over long-term collection. Under these conditions, VI-ReID methods, built on a heterogeneous-modality retrieval paradigm, suffer from three trustworthiness challenges: matching conflicts due to high homogeneous-modality similarity, interference from modality uncertainty, and robustness degradation induced by unknown modality combinations. They fail to meet the requirements of trustworthy visual recognition in reliability, consistency, and dynamic adaptability. To address these challenges, we formalize the Visible-Infrared Modality-Incomplete Re-Identification (VIMI-ReID) task. We reorganize existing datasets to construct the SYSU-VIMI and RegDB-VIMI benchmarks. The unpredictable modality combinations and inherent similarity of homogeneous-modality samples in VIMI-ReID cause a significant performance drop in existing VI-ReID methods. We propose the Modality Adaptive Matching Transformer (MAMT). It employs a Divergence Transformer Module (DTM) and a Shared Transformer Module (STM) to extract modality-specific and modality-shared features, respectively. Guided by a divergence loss, the DTM enriches modality-specific features with modality-style information to enhance discriminability within the same modality. A Modality Adaptive Matching Module (MAM) dynamically fuses features according to the query-gallery modality relationship, enabling stable matching under arbitrary and uncertain modality conditions. Extensive experiments on the VIMI benchmarks demonstrate the effectiveness and adaptability of MAMT.
https://arxiv.org/abs/2607.18688
Robotic perception pipelines increasingly rely on large vision backbones deployed on SWaP-constrained edge platforms, making post-training quantization (PTQ) attractive for real-time inference. However, while PTQ often preserves clean in-distribution accuracy, we show that it can substantially degrade reliability under deployment-relevant distribution shifts (e.g., sensor noise, severe weather, and novel operating environments), creating a Quantization-Induced Robustness Gap. Across foundational vision benchmarks (ImageNet-C and PACS), 4-bit PTQ models exhibit pronounced robustness degradation despite negligible ID accuracy loss. To address this, we propose Recti-Q, a lightweight feature-space rectification framework that freezes the quantized backbone and trains a small classifier-head LoRA adapter using only source data. Recti-Q is architecture-agnostic across CNNs and Transformers, supports efficient teacher-free training, and recovers a significant portion of the lost robustness, in some cases matching or exceeding FP32 performance. At less than 1% parameter overhead (as small as 6 KB), Recti-Q preserves over 99% of PTQ memory savings, adds negligible compute, and enables low-bandwidth Over-The-Air (OTA) resilience patching for deployed robotic fleets operating in unpredictable physical environments.
https://arxiv.org/abs/2607.18540
Robots in cluttered indoor spaces often fail not because they cannot generate collision-free paths, but because a fixed safety margin is mis-calibrated: conservative margins cause detours and timeouts, while permissive margins lead to near-boundary shortcuts under perception bias. Diffusion-based planners propose diverse trajectory candidates from egocentric RGB-D, yet reliable selection remains the bottleneck. We propose a context-conditioned safety critic that learns an adaptive clearance preference for ranking diffusion proposals, decomposed into three complementary terms: (i) a safety term with a clearance-budget penalty and a control-barrier-function residual for waypoint- and transition-wise safety, (ii) an efficiency term combining a smoothness penalty with a safety-gated detour-ratio penalty that avoids detours without incentivizing risky shortcuts, and (iii) a distance-constraint matching term that anchors the learned budget to realized ESDF clearances to prevent margin collapse. We train the critic with privileged ESDF geometry in simulation and distill it into a perception-only selector via a two-stage teacher-student procedure. On PointGoal navigation in HM3D and MP3D, including cross-dataset transfer, our method achieves the highest success rate (SR) and success weighted by path length (SPL) among strong diffusion, optimization, and RL baselines. Trained purely in simulation, it transfers to a Unitree G1 humanoid and navigates cluttered indoor scenes without task-specific tuning.
https://arxiv.org/abs/2607.18200
Unlike conventional video game development, which relies on labor-intensive pipelines for asset production, animation, physics, and programming, video world models generate interactive environments from user inputs instantly. It enable us to create customized, explorable, and continuously evolving virtual world from text, an image, or video. Realizing this vision requires four tightly coupled capabilities: interaction, persistent spatiotemporal consistency, stable long-horizon generation, and efficient response. We present AlayaWorld, an interactive long-horizon video world model that generates 24-fps video at 540p and 720p. Built on a 15B video diffusion transformer, AlayaWorld generates short latent chunks autoregressively under camera trajectories and switchable text prompts. Its bounded visual context combines a persistent sink frame, compressed temporal history, geometry-aligned spatial memory, and recent-frame conditioning. To reduce long-term drift, the model is trained with corrupted histories and prediction residuals collected from its own roll-outs. We further introduce a discrete autoregressive distillation formulation that combines distribution-matching distillation, self-forcing++, and consistency distillation, reducing inference from approximately 30 sampling steps to four steps per chunk. On iWorld-Bench, AlayaWorld achieves the best performance over long-horizon generation. Conceived as a full-stack, open-source, and long-term project, AlayaWorld is intended to provide an extensible foundation for future research on interactive video world models.
https://arxiv.org/abs/2607.18367
Standard evaluation of many recognition systems contains distribution shift by construction, since benchmarks place disjoint conditions in the training and test splits. Under such a shift, split conformal prediction keeps marginal coverage near the nominal level while per-class coverage fails silently: on a real cross-subject skeleton benchmark, marginal coverage stays near ninety percent, the worst action class is covered about seventy percent of the time, and ten of the sixty classes fall below eighty percent coverage. We characterize the cost of restoring per-class validity. First, an impossibility: once the shift acts jointly on the covariates and the labels, the target class-conditional score law is unidentified from source labels and an unlabeled target sample, so no label-free method attains per-class coverage that is at once valid and efficient. Second, we make the cost precise: per-class validity alone needs only a handful of target labels per class, while the label count necessary and sufficient for validity together with per-class efficiency grows as the inverse square of the efficiency tolerance and the logarithm of the number of classes, with matching upper and lower bounds. Third, within the evaluated prediction-powered inference family, even the most favorable use of the classifier's own pseudo-labels on an unbounded unlabeled target pool improves efficiency by at most a small constant factor where coverage collapses. Skeleton action recognition is our real-data case study. A per-class calibration using source labels alone recovers a substantial share of the per-class gap while the shift preserves marginal coverage, and stops helping exactly when marginal coverage itself breaks. Three real shifts of increasing severity trace this boundary, and the same collapse and recovery appears on a natural-image corruption benchmark, beyond any single modality.
https://arxiv.org/abs/2607.18088
Many visual reinforcement learning (RL) algorithms learn representations by matching latent distances to a behavioral distance induced by reward and transition similarity. In practice, the choice of the latent distance can strongly affect performance: using a fixed, pre-specified global norms (e.g., $\ell_p$ norms or other hand-designed metrics) may be overly restrictive to capture the behavioral distance. In contrast, unconstrained pairwise distances may admit degenerate solutions that drive the metric loss down without improving the representation. To address this gap, we introduce **PAMD: Pairwise Adaptive Mahalanobis Distance**, which parameterizes a positive-definite, pair-conditioned metric for measuring latent state similarity. PAMD is a simple plug-in for existing bisimulation-based methods, offering a more expressive yet structured alternative to fixed, pre-specified latent distances. We empirically validate our method on visual MuJoCo continuous-control tasks, where final performance of several recent bisimulation-based RL algorithms is substantially improved when equipped with the distance we propose.
https://arxiv.org/abs/2607.18004