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When computing indirect illumination, what happens when one of your secondary rays from a diffuse material happens to hit a light source? Is it possible that you are doubling up on your direct illumination? One quick experiment might be to double the intensity of your light source, omit direct illum...

Offhand it looks like your LSE (possibly LS(S|D)*E) paths are broken. How are you calculating direct lighting on specular surfaces? If you're doing explicit connections to the light source (e.g., picking a point on the source, casting a shadow ray, and evaluating the BSDF), then the specular compone...

Importance is a necessity for any renderer that traces more than one bounce after tracing a ray from the camera. For example, in a simple path tracer, the "weight" of an eye subpath is accumulated importance divided by the accumulated pdf. At each bounce, the importance is reduced by the B...

Without the We term, W(x,w) would just be zero (since some nonzero portion of light hitting a reflective surface would be absorbed). Importance is basically what portion of reflected or emitted light from a surface contributes to a rendered image. In a path-/ray-tracer We(x,w) should generally only ...