|Fig. 1: The Deuterium-Tritium reaction.  (Source: Wikimedia Commons)|
Nuclear fusion is the name for a chemical process by which two atoms collide with sufficient energy to fuse together into one atom. The easiest fusion reaction to achieve is one between two different isotopes of Hydrogen - Deuterium (Hydrogen with one neutron) and Tritium (Hydrogen with two neutrons) - that comprise two protons and three neutrons in total. The products are a Helium atom (two protons and two neutrons) and a lone neutron that has an energy of 14.1 MeV (See Fig. 1).
This lone neutron is essential to understanding both the potential and the dangers of nuclear fusion. On one hand, it can create energy by heating up water to power a steam turbine; this is how normal nuclear power plants operate right now, except their neutrons are produced by nuclear fission rather than nuclear fusion. On the other hand, this neutron also has enough energy to make U-238 (harmless on its own) into Pu-239, which can be material for a nuclear bomb; in other words, this lone neutron can be used to make "fissile material." The same process applies to Th-232, which can be made into U-233.
Why is it important that the Deuterium-Tritium (DT) reaction can produce fissile material? The state of world politics right now is such that the easiest and most effective way to stop nuclear bombs from being built is to restrict access to fissile material. The International Atomic Energy Agency has even set limits of what it considers to be "significant quantities" of fissile materials that form the lower limit of what could be used to make a nuclear bomb.
There are two main ways that nuclear fusion can be dangerous: firstly, the more we understand nuclear fusion, the easier it is to build a weapon that incorporates fusion. That risk is hard to quantify because of the restrictions on weapons knowledge, and thus will not be addressed in this report. The second way that fusion can be dangerous is through its ability to produce fissile material which could then be used in a nuclear bomb. Because fission produces so much more energy (~200 MeV vs ~17 MeV) per reaction, it makes more sense for bomb makers to use fission for most of the destructive power than to use fusion.
The easiest way to produce fissile material would be to use a fusion-fission hybrid system, which is an idea in which you combine fusion and fission reactions in order to produce both energy and fissile material.  But, fusion-fission hybrids face an uphill battle engineering-wise and may never become a commercial product because the performance probably wouldn't justify the extra cost over a normal fission system.  The more likely scenario is that a fusion reactor is modified to become a breeder of fissile material, as is examined in Glaser and Goldston's 2012 paper. 
The first question we need to answer is how much fusion products are created. Glaser and Goldston put a high estimate on hybrid production at 2.85 kg of fissile material per MW-year of fusion energy. Their estimate for a modified fusion reactor is much smaller; they ran a simulation on a 2 GWt fusion plant and found that it could produce 20 kg per week. That is enough for almost three nuclear bombs per week, which definitely qualifies as a proliferation risk. On the bright side, Glaser and Goldston highlight that it would take weeks to refit a fusion reactor for breeding, and that we can take precautions when building larger reactors to make sure that they are much more difficult to outfit for breeding. 
Purely from the amount of fissile material that can be produced by fusion, we can safely label it as a proliferation risk. It is possible to take steps to reduce these risks, but we should keep in mind that the battle to stop nuclear proliferation will not end if nuclear fusion is discovered; rather, it will just take on a new dimension as the possibility of breeding becomes a much larger threat.
© John Stayner. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 J. Kates-Harbeck, "The Fusion-Fission Hybrid," Physics 241, Stanford University, Winter 2011.
 J. P. Friedberg and A. C. Kadak, "Fusion-Fission Hybrids Revisited," Nat. Phys. 5, 370 (2009).
 A. Glaser and R. J. Goldston, "Proliferation Risks of Magnetic Fusion Energy: Clandestine Production, Covert Production and Breakout," Nucl. Fusion, 52, 043004 (2012).