\documentclass[]{memoir}

\usepackage[pdftex]{graphicx}
%\usepackage[capitalise]{cleveref}
\usepackage{varioref}
\newsubfloat{figure}

%\usepackage{subfig}

\begin{document}

%\mainmatter
%\renewcommand{\thefigure}{\thechapter.\arabic{figure}}

\chapter{Hello}

\begin{figure}
\subbottom[Caption 1]{\includegraphics[width=2.0in]{xw.png}\label{dnf-fig-a}}
\subbottom[Caption 2]{\includegraphics[width=2.0in]{xw.png}\label{dnf-fig-b}}
\caption{This is overall caption\label{dnf-fig}.}
\end{figure}


\chapter{World}

This is a ref to subbottom~\vref{dnf-fig-a}.

This is a ref to next subbottom~\ref{dnf-fig-b}.

More random text here~\ref{dnf-fig}.

\end{document}