SymRegFlow: Symmetry-Regularized Flow Matching for Video World Models

Flow-matching models generate samples through iterative velocity predictions, but typically do not revisit these predictions using the intermediate representations that produced them. We introduce CorrFlow, a self-correcting flow-matching framework that reuses this information through a lightweight refiner. Under rectified-flow interpolation, the error of the one-step clean prediction equals the realized velocity residual scaled by the noise level. Motivated by this identity, the refiner learns to predict residual corrections from the base model's clean prediction, conditioning, noise level and hidden states from the same forward pass. The correction is added to the base velocity before each sampling update, so subsequent predictions are made from the corrected state. This requires no additional base-model evaluations and only one lightweight refiner evaluation per step. Our theoretical analyses establish conditions under which feature reuse outperforms raw-input affine predictors and refiner training achieves greater residual-risk reduction than continued base-model training under a matched training compute budget. Experiments on class-conditional image generation, text-to-video generation and image-to-video generation show consistent improvements over the corresponding base models, including gains in visual quality and physical consistency. Project Page: https://fogradio.github.io/corrflow-project

Generating geometrically consistent videos remains an open challenge: text-to-video diffusion models trained on web-scale data treat geometry only implicitly, leading to object deformation, texture drift, and non-rigid backgrounds under camera motion. Existing solutions either improve consistency as a byproduct, apply only to static scenes or realign the latent space of the model completely. We introduce a geometry-consistency reward that directly measures whether motion in a generated video is compatible with a coherent scene. Our key insight is that in physically consistent videos, background motion should be explainable by rigid camera-induced flow, while independently moving objects should preserve appearance identity along motion trajectories. We operationalize this using optical flow, depth--pose predictions, and feature-based correspondence to separate rigid and dynamic regions and evaluate their respective consistency. Integrating this reward with reinforcement fine-tuning transforms geometric consistency from an emergent property into an explicit optimization objective for video generators. The approach is model agnostic and applies to diverse dynamic scenes containing both camera and object motion. Experiments show substantial reductions in temporal geometric artifacts over strong baselines while preserving perceptual quality. Code and model weights are published.

Novel view synthesis from sparse images must reconcile faithful reconstruction of observed regions with plausible completion of unseen content, while maintaining world consistency across viewpoints. Existing geometry-based methods preserve observed scene structure but often struggle to complete unseen regions, whereas video generative models offer rich appearance priors but accumulate inconsistencies during sequential view generation. We propose GeoVerse, a framework that synthesizes world-consistent novel views by performing generation within the geometric latent space of a pretrained 3D foundation model and injecting appearance priors from a video generative model. Specifically, GeoVerse extracts multilevel features from Wan2.2 VACE and injects them into the geometric latent diffusion model via a ControlNet-style adapter, incorporating video-learned appearance priors to enhance structural completion. To enforce cross-view coherence, a global spatial memory continuously aggregates observed and synthesized content, reprojecting target-aligned guidance to anchor subsequent predictions to a shared scene representation. Extensive experiments across diverse datasets demonstrate improved visual quality and geometric consistency, with a 2.23 dB higher PSNR on DL3DV and 32.4% lower ATE on Mip-NeRF360 compared to GLD.