Reaction between manganese(IV) oxide and sulfuric acid
I am afraid I cannot provide the exact mechanism. Nevertheless, here is what I know.

The reaction is most certainly more complex than the equation

$$\ce{2 MnO2_{(s)} + 2 H2SO4_{(aq)} -&gt; 2 MnSO4_{(aq?)} + 3 O2_{(g)} + H2O_{(l,g)}}$$

suggests. One might say it is even misleading, but it is definitely not the whole story.


A purple smoke


After adding concentrated sulfuric acid to manganese(IV) oxide, a purplish smoke manifests. This suggests to the species $\ce{MnO4-}$. Yet, what is the balancing particle? Is it $\ce{Mn^2+}$, or rather $\ce{H}$? I have no clue.
$$\ce{2 Mn_{(aq)}^2+ + 5 MnO2_{(s)} + 6 H3O+_{(aq)} -&gt; 2 HMnO4_{(aq)} + 5 Mn^2+_{(aq)} + 8 H2O_{(l,g)}}$$


A green to brown mixture


The initial mixture is green. This points to either $\ce{MnO4^2-}$ or $\ce{Mn2O7}$, even $\ce{MnO4^3-}$ could be it. Again, which one is it? Maybe it is all of the above? Upon standing, we observe a brown precipitate. The manganese(IV) oxide appears to reform … Speculation (more in the next chapter):

$$\ce{MnO4_{(aq)}^2- + H2SO4_{(aq)} -&gt; H2MnO4_{(aq)} + SO4_{(aq)}^2-}\\\ce{3 H2MnO4_{(aq)} -&gt;  2 HMnO4_{(aq)} + MnO2_{(s)} + 2 H2O_{(l,g)}}$$

$$\ce{3 MnO4^2- + 2 H2O_{(l)} -&gt; 2 MnO4- + MnO2_{(s)} + OH_{(aq)}-}$$


Oxygen, where's that from?


I did the classic match experiment; it did indeed burn more vigorously near the reaction mixture.

$$\ce{HMnO4_{(aq)} -&gt; MnO2_{(s)} + 3 O2_{(g)} + 2 H2O_{(l,g)}}$$
$$\ce{2 MnO4^2- -&gt; MnO4^3- + MnO2_{(s)} + O2_{(g)}}$$
$$\ce{2 Mn2O7_{(l)} -&gt; 4 MnO2_{(s)} + 3 O2_{(g)}}$$


I think you get the idea


Sorry I could not be of more assistance. The mixture is indeed complex with multiple processes happening in parallel. (This is actually the case with every reaction.) It should at least point you in some direction.


Extra


I was a bit loosey–goosey with the ionic equations; you should not do that ;). In my opinion, it made the process more clear.
One might also wish to consider $\ce{Mn2MnO4}$ or $\ce{Mn3O4}$ which, I believe, are also brown.