cs.LGOct 21, 2026

ART-MPG: Autoregressive R/T Manifold Path Guiding

Authors: Zehao Zhao, Yanyang Yang, Xiaole Zhang, Xiyu Deng

Organizations: Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California · Computational Science and Engineering, Georgia Institute of Technology · Department of Electrical and Computer Engineering, Carnegie Mellon University

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Abstract

Specular chains concentrate important transport in small regions of path space and the structure depends on chain topology. We introduce ART-MPG, a compact neural model that samples chain length, an autoregressive reflection/transmission (R/T) string, and a direction from a topology-conditioned four-component von Mises-Fisher (vMF) mixture. We extend the repeated trial weighting in Manifold Path Guiding (MPG) by conditioning retry sampling on both chain length and the sampled R/T string, accounting for its known mass outside the stochastic re-hit trials. For a fixed proposal and target chain, this preserves the ideal expectation while reducing the expected retry count and reciprocal-estimator variance compared with retries conditioned on chain length alone. We distinguish the formal unbiasedness result from the capped and clamped renderer used in experiments. We evaluate fourteen scenes across a range of samples per pixel (SPP) against existing online and offline rendering algorithms. Our method consistently produces lower mean squared error at equal SPP than the online and offline baselines, with lower standard deviation across runs.

Figures & tables

Figure 1: Equal-SPP results for Living , Water , Stone , and Pool , from top to bottom. Curves show median full-frame MSE across ten fixed runs; 60-SPP annotations additionally show sample standard deviation. Image crops come from one fixed 60-SPP visualization run, whereas quantitative values use separate 64×6464\times 64 full-frame renders. The displayed crops are not median images.
 BaselinesOurs
ScenePTPPGSMSMPGNPMART-MPG
Living1.227×10−31.227\times 10^{-3}4.710×10−24.710\times 10^{-2}1.206×10−31.206\times 10^{-3}1.676×10−31.676\times 10^{-3}1.463×10−31.463\times 10^{-3}1.003×10−3\mathbf{1.003\times 10^{-3}}
Lamp4.009×10−24.009\times 10^{-2}3.202×10−23.202\times 10^{-2}6.472×10−36.472\times 10^{-3}1.780×10−31.780\times 10^{-3}2.483×10−32.483\times 10^{-3}1.683×10−3\mathbf{1.683\times 10^{-3}}
Plane2.912×10−12.912\times 10^{-1}2.914×10−12.914\times 10^{-1}2.992×10−12.992\times 10^{-1}2.810×10−12.810\times 10^{-1}2.896×10−12.896\times 10^{-1}2.728×10−1\mathbf{2.728\times 10^{-1}}
Slabs1.112×10−11.112\times 10^{-1}2.340×1012.340\times 10^{1}8.095×10−28.095\times 10^{-2}2.823×10−12.823\times 10^{-1}7.957×10−27.957\times 10^{-2}6.479×10−2\mathbf{6.479\times 10^{-2}}
Stone7.035×1007.035\times 10^{0}3.196×10−23.196\times 10^{-2}2.558×10−22.558\times 10^{-2}9.165×10−29.165\times 10^{-2}2.505×10−22.505\times 10^{-2}1.897×10−2\mathbf{1.897\times 10^{-2}}
Table 1: Median full-frame linear-RGB MSE across D01–D10 for each scene at 60 SPP and 64×6464\times 64 resolution. Lower is better.
Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

 BaselinesOurs
ScenePTPPGSMSMPGNPMART-MPG
 Cell order: median / mean / sample SD; MSE ↓\downarrow
Living1.227 ⁣× ⁣10−31.227\!\times\!10^{-3} 1.423 ⁣× ⁣10−31.423\!\times\!10^{-3} 5.596 ⁣× ⁣10−45.596\!\times\!10^{-4}4.710 ⁣× ⁣10−24.710\!\times\!10^{-2} 4.711 ⁣× ⁣10−24.711\!\times\!10^{-2} 2.403 ⁣× ⁣10−42.403\!\times\!10^{-4}1.206 ⁣× ⁣10−31.206\!\times\!10^{-3} 1.769 ⁣× ⁣10−31.769\!\times\!10^{-3} 1.775 ⁣× ⁣10−31.775\!\times\!10^{-3}1.676 ⁣× ⁣10−31.676\!\times\!10^{-3} 2.739 ⁣× ⁣10−32.739\!\times\!10^{-3} 2.046 ⁣× ⁣10−32.046\!\times\!10^{-3}1.463 ⁣× ⁣10−31.463\!\times\!10^{-3} 1.593 ⁣× ⁣10−31.593\!\times\!10^{-3} 5.804 ⁣× ⁣10−45.804\!\times\!10^{-4}1.003 ⁣× ⁣10−3\mathbf{1.003\!\times\!10^{-3}} 1.008 ⁣× ⁣10−3\mathbf{1.008\!\times\!10^{-3}} 5.380 ⁣× ⁣10−55.380\!\times\!10^{-5}
Lamp4.009 ⁣× ⁣10−24.009\!\times\!10^{-2} 4.003 ⁣× ⁣10−14.003\!\times\!10^{-1} 5.886 ⁣× ⁣10−15.886\!\times\!10^{-1}3.202 ⁣× ⁣10−23.202\!\times\!10^{-2} 6.495 ⁣× ⁣10−16.495\!\times\!10^{-1} 1.140 ⁣× ⁣1001.140\!\times\!10^{0}6.472 ⁣× ⁣10−36.472\!\times\!10^{-3} 6.468 ⁣× ⁣10−36.468\!\times\!10^{-3} 2.226 ⁣× ⁣10−52.226\!\times\!10^{-5}1.780 ⁣× ⁣10−31.780\!\times\!10^{-3} 1.869 ⁣× ⁣10−31.869\!\times\!10^{-3} 3.708 ⁣× ⁣10−43.708\!\times\!10^{-4}2.483 ⁣× ⁣10−32.483\!\times\!10^{-3} 2.493 ⁣× ⁣10−32.493\!\times\!10^{-3} 5.206 ⁣× ⁣10−45.206\!\times\!10^{-4}1.683 ⁣× ⁣10−3\mathbf{1.683\!\times\!10^{-3}} 1.776 ⁣× ⁣10−3\mathbf{1.776\!\times\!10^{-3}} 4.036 ⁣× ⁣10−44.036\!\times\!10^{-4}
Plane2.912 ⁣× ⁣10−12.912\!\times\!10^{-1} 6.499 ⁣× ⁣1026.499\!\times\!10^{2} 2.054 ⁣× ⁣1032.054\!\times\!10^{3}2.914 ⁣× ⁣10−12.914\!\times\!10^{-1} 2.914 ⁣× ⁣10−12.914\!\times\!10^{-1} 1.935 ⁣× ⁣10−41.935\!\times\!10^{-4}2.992 ⁣× ⁣10−12.992\!\times\!10^{-1} 3.396 ⁣× ⁣10−13.396\!\times\!10^{-1} 1.453 ⁣× ⁣10−11.453\!\times\!10^{-1}2.810 ⁣× ⁣10−12.810\!\times\!10^{-1} 2.982 ⁣× ⁣10−12.982\!\times\!10^{-1} 5.881 ⁣× ⁣10−25.881\!\times\!10^{-2}2.896 ⁣× ⁣10−12.896\!\times\!10^{-1} 2.903 ⁣× ⁣10−12.903\!\times\!10^{-1} 1.307 ⁣× ⁣10−21.307\!\times\!10^{-2}2.728 ⁣× ⁣10−1\mathbf{2.728\!\times\!10^{-1}} 2.721 ⁣× ⁣10−1\mathbf{2.721\!\times\!10^{-1}} 3.023 ⁣× ⁣10−33.023\!\times\!10^{-3}
Slabs1.112 ⁣× ⁣10−11.112\!\times\!10^{-1} 9.797 ⁣× ⁣1019.797\!\times\!10^{1} 2.714 ⁣× ⁣1022.714\!\times\!10^{2}2.340 ⁣× ⁣1012.340\!\times\!10^{1} 2.464 ⁣× ⁣1012.464\!\times\!10^{1} 2.774 ⁣× ⁣1012.774\!\times\!10^{1}8.095 ⁣× ⁣10−28.095\!\times\!10^{-2} 8.245 ⁣× ⁣10−28.245\!\times\!10^{-2} 6.680 ⁣× ⁣10−36.680\!\times\!10^{-3}2.823 ⁣× ⁣10−12.823\!\times\!10^{-1} 4.073 ⁣× ⁣10−14.073\!\times\!10^{-1} 3.124 ⁣× ⁣10−13.124\!\times\!10^{-1}7.957 ⁣× ⁣10−27.957\!\times\!10^{-2} 8.116 ⁣× ⁣10−2\mathbf{8.116\!\times\!10^{-2}} 4.288 ⁣× ⁣10−34.288\!\times\!10^{-3}6.479 ⁣× ⁣10−2\mathbf{6.479\!\times\!10^{-2}} 9.854 ⁣× ⁣10−29.854\!\times\!10^{-2} 7.204 ⁣× ⁣10−27.204\!\times\!10^{-2}
Appendix
Table A1: Combined 60-SPP 64 ×\times 64 full-frame linear-RGB MSE summaries across D01–D10 ( n=10n=10 per cell). Each method cell lists median, arithmetic mean, and sample standard deviation from top to bottom. Row-minimum medians and means are bold; SD is not ranked.
Figure A1: Median MSE summaries for Sphere (top) and Lamp (bottom).
Figure A2: Median MSE summaries for Plane (top) and Slabs (bottom).
Figure A3: Median MSE summaries for Ring-and-Slab (top) and Pillars (bottom).
Figure A4: Median MSE summaries for Slab- ×1\times 1 (top) and Slab- ×3\times 3 (bottom).
Figure A5: Median MSE summaries for Pillar- ×3\times 3 (top) and Cornell Glass (bottom).
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