In this work, we introduce the Geometric Diffusion Bridge (GDB), a novel generative modeling framework that accurately bridges initial and target geometric states.

Our idea is to replace typical neuron's response in the firsthiddenlayerbyitsexpected value. Thisapproach canbeappliedforvarious types ofnetworksatminimal costintheirmodification. Moreover,incontrast to recent approaches, it does not require complete data for training. Experimental results performed ondifferent types ofarchitectures showthatourmethod gives better results than typical imputation strategies and other methods dedicated for incompletedata.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Inthiswork,wepropose sampling-argmax, adifferentiable training method that imposes implicit constraints tothe shape of the probability map by minimizing the expectation of the localization error.

Next consider the case where[ti,ti+1] lies in a range[t`,tr] over which the camera ray is exiting the surface, i.e. the signed distance function is increasing onp(t) over [t`,tr]. Then we have ( f(p(t)) v) < 0 in [ti,ti+1]. Then, according to Eqn. 1, we haveρ(t) = 0. Therefore, by Eqn.12ofthepaper,wehave αi=1 exp Recall that our S-density fieldφs(f(x)) is defined using the logistic density functionφs(x) = se sx/(1+e sx)2, which is the derivative of the Sigmoid functionΦs(x) = (1+e sx) 1, i.e. φs(x)=Φ0s(x). As a first-order approximation of signed distance functionf, suppose that locally the surface is tangentially approximated byasufficiently small planar patch with itsoutwardunitnormal vector denotedas n. Nowsupposep(t)isapoint on the surfaceS,that is, f(p(t)) = 0. Next we will examine the value ofdwdt(t) at t = t . Thesigneddistancefunction f ismodeledbyanMLP that consists of 8hidden layers with hidden size of 256.