Nuclear fusion leads to conversion of a small amount of mass in to energy. However, no (or a few) physical phenomenon appears to convert energy into mass.
As we have so many stars with large scale fusion occurring at the core. Is the net mass of the universe decreasing?
I found a relevant note on black holes, which says:
As per Hawking: The matter is converted to energy and some of the energy gets converted to equal amounts of matter and antimatter, the matter goes out of the black hole, but the antimatter goes inside the black hole and in turn decreases its mass. Ultimately after millions or even billions of years, the black hole will be evaporated away. completely. So that means every matter that goes into the black hole is responsible for its destruction.
Best Answer
Dealing with the example of an isolated star. During its life, nuclear fusion ultimately results in radiation from the photosphere that carries energy into space. As a result the mass of the star must decrease, because the total mass-energy is conserved.
However, another property that is conserved is the baryon number (the total number of protons and neutrons). How is this number conserved yet the mass decreases? The answer is that the baryons get together as more massive nuclei with negative binding energy.
If we now look at a co-moving volume in the universe (that is a box that expands in proportion to the universe as a whole), then more and more hydrogen and helium is fused into heavier elements which reduces the amount of mass in the form of atoms and nuclei. However this is partially made up for by the radiated energy (divided by $c^2$) in the form of photons and neutrinos which is in the box.
I say partially, because stellar remnants like neutron stars and white dwarfs have negative gravitational binding energy that reduces their gravitational mass.
All this pales into utter insignificance compared to other cosmological phenomena going on in the box. The radiation energy density decreases as the scale factor to the power four, so the co-moving radiation energy decreases with the scale factor. The radiation energy density is however much smaller than the matter density (at any epoch when stars can form), which in turn is smaller than the energy density of the vacuum (aka dark energy). The vacuum energy density appears to be constant. This means that the vacuum energy in a co-moving volume increases as the cube of the scale factor.
So to sum up, what is commonly referred to as "mass" will decrease (slightly), but the total mass/energy appears to be increasing roughly as the cube of the scale factor.