Every Dog Has Its Day, Probably: A Balanced Synthetic Benchmark and Probabilistic Modeling for 3D Dog Pose Estimation

3D dog pose estimation is hindered by two limitations in ex-isting benchmarks: distributional bias toward canonical viewpoints, sta-ble poses, and narrow morphologies, and alignment degradation betweenimages and 3D annotations. We instead synthesize a large-scale bal-anced benchmark (4.2M images with exact 3D ground truth) by decou-pling pose, shape, and texture into independent libraries (70K retargetedposes, 500 breed shapes, 1,000 appearance maps) and rendering directlyto guarantee pixel-perfect alignment and broad view coverage. However,this balanced distribution exposes a challenge previously masked by bi-ased data: non-canonical combinations of pose, shape, and viewpointcreate multimodal 3D ambiguities that deterministic regression cannotresolve. We therefore propose a flow-based probabilistic framework thatmodels the conditional distribution of 3D poses given an image, pro-ducing multiple plausible hypotheses under ambiguity while convergingto precise estimates for clear views. Experiments on StanfordExtra, An-imal3D, and our synthetic benchmark demonstrate that our method,trained solely on synthetic data, outperforms state-of-the-art approaches(79.9 vs. 33.2 PCK on the synthetic benchmark). Dataset available here.