ReSTIR — Reservoir-based Spatiotemporal Importance Resampling
Bitterli et al. 2020 — one of the most impactful real-time rendering papers.
Enables high-quality direct lighting with thousands of lights at real-time rates.
Parent: PathTracer Learning
The Problem ReSTIR Solves
Direct lighting with many lights
Naive: sample one random light per pixel → high variance with many lights
Better: sample proportional to light contribution → need to evaluate all lights
ReSTIR: efficiently find good light samples by resampling candidates
Key insight
Resampled Importance Sampling (RIS): generate M candidates, select 1 proportional to target PDF
Reservoir: compact data structure to maintain RIS state
Temporal reuse: reuse reservoir from previous frame (free extra samples)
Spatial reuse: share reservoirs with neighbors (more free samples)
Resampled Importance Sampling (RIS)
Goal: sample from target distribution p̂(x) when direct sampling is hard
Algorithm
Generate M candidates {x_1, ..., x_M} from source distribution q(x)
Select one candidate with probability proportional to w_i = p̂(x_i) / q(x_i)
The selected sample approximates sampling from p̂
Weight formula
W = (1/M) * Σ w_i — sum of weightsUnbiased contribution weight: W_selected = W / p̂(x_selected)
In practice for direct lighting
q(x) = uniform over all lights (easy to sample)p̂(x) = L_e(x) * G(x) * V(x) — emission × geometry × visibilityVisibility V(x) is expensive — defer to final evaluation
The Reservoir Data Structure
Compact structure per pixel
struct Reservoir {
LightSample y; // current selected sample
float w_sum; // sum of weights seen so far
int M; // number of candidates processed
float W; // unbiased contribution weight
};
Streaming update (one candidate at a time)
void update(Reservoir r, LightSample x, float w):
r.w_sum += w
r.M += 1
if random() < w / r.w_sum:
r.y = x // replace selected sample
Merging two reservoirs
Reservoir merge(Reservoir a, Reservoir b):
combined = new Reservoir()
update(combined, a.y, p̂(a.y) * a.W * a.M)
update(combined, b.y, p̂(b.y) * b.W * b.M)
combined.M = a.M + b.M
combined.W = combined.w_sum / (p̂(combined.y) * combined.M)
return combined
ReSTIR DI Algorithm (per frame)
Pass 1: Initial candidates
For each pixel: sample M=32 light candidates from q (uniform)
Store in reservoir
Pass 2: Temporal reuse
Reproject previous frame’s reservoir to current pixel
Merge current reservoir with reprojected reservoir
Cap M to prevent unbounded growth (M_max = 20 typically)
Pass 3: Spatial reuse
For each pixel: sample K=5 neighboring pixels
Merge their reservoirs into current pixel’s reservoir
Apply MIS weights to avoid bias from different pixel domains
Pass 4: Shading
Evaluate visibility for final selected sample (one shadow ray)
Compute shading: L = f_r * L_e * G * V * W
Bias in ReSTIR
Naive spatial reuse is biased
Neighbor’s reservoir was selected for neighbor’s domain, not current pixel
Using it directly introduces bias (incorrect PDF)
Correction methods
MIS-based resampling (Talbot 2005) — correct but expensive
Pairwise MIS (Bitterli 2022) — efficient and unbiased
1/M heuristic — biased but fast, often acceptable
ReSTIR GI (Global Illumination)
Extends ReSTIR to indirect lighting
Each reservoir stores a full path segment (not just a light)
Temporal and spatial reuse of path segments
Much more complex bias correction needed
Paper: “ReSTIR GI: Path Resampling for Real-Time Path Tracing” (Ouyang et al. 2021)
Implementation Notes
Two reservoir buffers needed (ping-pong for temporal)
Spatial reuse needs neighbor reservoirs from same frame (not current pass)
Use a separate spatial pass reading from temporal output
Visibility reuse: cache shadow ray results to avoid redundant traces