data = RandomFunction[WienerProcess[0, 1], {0, 1, 0.01}, 1000];
data // Normal // #[[All, 2]] & /@ # & // Set[sample, #] &;

Table[Transpose@{sample[[All, i]], sample[[All, i + 1]]}, {i, 1,
      99}] // Flatten[#, 1] & // KernelMixtureDistribution //
  Set[pxy, #] &;
px = MarginalDistribution[pxy, 1];
pcxy = PDF[pxy, {0, y}]/PDF[px, 0];

ProbabilityDistribution[pcxy, {y, -Infinity, Infinity}]
RandomVariate[%, 3] // AbsoluteTiming