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I noticed recently that there is a new option in Cycles for "branched path tracing", can someone explain what this does in easy to understand terms? Should we expect faster render times or less samples etc?

Can you give examples of best uses?

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The Branched path integrator is not new, it was renamed from the Non-Progressive integrator in 2.69.
From the manual:

The branched path tracing integrator (formerly called non-progressive integrator) is similar, but at the first hit it will split the path for different surface components and will take all lights into account for shading instead of just one. This makes each sample slower, but will reduce noise, especially in scenes dominated by direct or one-bounce lighting. To get the same number of diffuse samples as in the path tracing integrator, note that e.g. 250 path tracing samples = 10 AA samples x 25 diffuse samples. The Sampling panel shows this total number of samples.

To visualize how this works, the Progressive integrator simulates one path (or ray) per sample:

enter image description here

The Branched path integrator splits the ray, sampling multiple directions as well as multiple components of the material (e.g. glossy, diffuse, etc) in one sample:

enter image description here

This is helpful because it takes into account light from multiple directions as opposed to only one, as well as giving more control over how different shaders are sampled. (this also helps reduce fireflies, see What is the Reason Cycles Creates Incorrectly Colored/Firefly Artifact Pixels?)

There is also a nice guide to using the Branched Path integrator with some comparisons written by Tomas Dinges.

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    $\begingroup$ I just found a really useful video explaining a neat process to go about setting up branched path tracing for a given scene: youtube.com/watch?v=YpTm-cwSuz4 I don't know what it is, but Blender's manual always seems really cryptic and unhelpful. This video helped clear up quite a bit of that for me. $\endgroup$ – Anson Savage Apr 6 '18 at 20:34
  • $\begingroup$ Thanks Anson, that video by Alex Petrov is the most helpful info I have ever learned since discovering Blender! :-) $\endgroup$ – Copperplate Apr 17 '18 at 17:07
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Branched Path Tracing is useful. Basically it allow you to focus render time on noisy areas, while saving time. It allows the user to focus render attention on a specific component of the render. If you have a lot of rough glossy materials in your scene but ver few diffuse you can increase the glossy samples individually without over rendering the diffuse part. CG Cookie made a video one this, unfortunately they do not think that it should be free. Also the Arnold Render's User Guide will explain very clearly how you can remove noise. This guide is written for maya.

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