To address this issue, [1] propose a Perp-Neg algorithm:

(cid:0)ϵpos − wnegϵneg

⊥(cid:1) ,

ϵpredict = ϵunc + wguidance
ϵneg = fdiffusion(xt; yneg, t) − ϵunc,

(8)

Figure 6: Comparison of the original sigmoid function with
its stretched variant (left) and the proposed scaled-sigmoid
function (right). With α < 1.0, the scaled-sigmoid function
possesses a broader high-gradient region, which accelerates
training.
of [0, 1]. However, we observe that applying the conven-
tional sigmoid to albedo causes difficulties in training con-
vergence. A deeper analysis reveals that the MLP output
may exceed the high-gradient region around zero, leading to
gradient vanishing. This phenomenon significantly impedes
the learning of the 3D representation, resulting in extended
training durations and occasional convergence failures.

To address this issue, we stretch the high-gradient region

by multiplying the input with a fractional coefficient α:

ˆfsigmoid(x) = fsigmoid(αx), α ∈ [0, 1].

(6)
Instant3D