Sensitivity as an Arbitrary Output Variable for Differentiable Rendering

2026-10-07

AI Summary

This study addresses the lack of intuitive representations for derivatives in differentiable rendering, which hinders their decomposition and inspection compared to primal images. We propose the Sensitivity AOV paradigm, drawing upon deferred shading principles to decouple the target camera from an inspection camera. Through a single backward pass, this method populates a scene-parameter sensitivity buffer, enabling multi-view readouts and fine-grained visualization of spatially varying parameters. By establishing derivatives as first-class rendering products, our approach successfully transforms abstract gradients into directly inspectable rendered outputs. Consequently, it significantly enhances both debugging efficiency and human–computer interaction capabilities within differentiable rendering systems.

Abstract

Differentiable renderers expose the derivative of any scalar objective with respect to every scene parameter, yet unlike the primal image, which decades of arbitrary output variables (AOVs) have taught us to decompose, inspect, and composite, these derivatives have no established representation for human inspection. We introduce the sensitivity AOV, a render output carrying the sensitivity of an objective to the scene parameters that influence it. A single reverse-mode pass populates a sensitivity buffer over the scene's parameter hierarchy, from which many views are read rather than re-differentiated, in direct analogy to deferred shading: image-space sensitivity at object and parameter-type granularity, projections onto a freely navigable scene from any inspection viewpoint, and, for spatially varying parameters, per-texel fields carried to the surface through texture coordinates. We separate the fixed camera that defines the objective from the free camera used to inspect the result, and position reverse-mode attribution against its forward-mode dual. Our aim is not a single algorithm but a scaffolding that establishes derivative outputs as first-class render products alongside the primal image.

Problem

• Differentiable Rendering
• Arbitrary Output Variables
• Sensitivity
• Derivative Representation
• Human Inspection

Innovation

• Differentiable Rendering
• Sensitivity AOV
• Reverse-mode Differentiation
• Deferred Shading
• Arbitrary Output Variables