Smoothness conjecture for homotopy fiber bundles with smooth total space

Let $f:X\to Y$ be a proper morphism of complex spaces. It is a homotopy fiber bundle if locally over $Y$ each fiber inclusion is a homotopy equivalence; it is a ${\mathbb Z}$-homology fiber bundle if the corresponding inclusions induce isomorphisms on homology with ${\mathbb Z}$ coefficients. Assume that $X$ is smooth. Smoothness conjecture. If $f$ is a homotopy or ${\mathbb Z}$-homology fiber bundle, then $f$ is smooth, and hence $f:X\to Y$ is a differentiable fiber bundle. The conjecture would identify the expected positive behavior for smooth varieties, in contrast with counterexamples for non-normal total spaces; the source does not provide a resolution.