τ = fsoftplus (fMLP(p; θ)[1]) ,
ρ = fsigmoid (fMLP(p; θ)[2 : 4]) ,

(1)

where τ ∈ R is volumetric density, indicating the opac-
ity of the scene geometry at the 3D coordinate. ρ ∈ R3
is the albedo, capturing the intrinsic colors that define the
scene. fMLP represents an MLP with parameters θ. [i : j]
denotes extracting channels from i to j. fsoftplus is the Soft-
plus activation function, ensuring positive volumetric den-
sity. fsigmoid is the sigmoid function, which confines the
albedo to the range of [0, 1]. These density and albedo val-
ues on a ray are then composited with volume rendering,
producing the RGB value for the pixel. We use a shad-
ing formulation similar to DreamFusion [23] in rendering.
Carrying out this process for all pixels on the image plane
results in the final rendered RGB image denoted as gθ(c),
which is parameterized by θ and conditioned on the camera
view c.

3.1.2 Score Distillation Sampling (SDS)
Instant3D