Filtration of gas containing oxidizer, to the reaction zone in a porous medium, due, e.g., to a buoyancy force or to an external pressure gradient, leads to the propagation of filtration combustion (FC) waves. The exothermic reaction occurs between the fuel component of the solid matrix and the oxidizer. In this paper, we analyze the ability of a reaction wave to propagate in a porous medium without the aid of filtration. We find that one possible mechanism of propagation is that the wave is driven by diffusion of oxidizer from the environment. The solution of the combustion problem describing diffusion driven waves is similar to the solution of the Stefan problem describing the propagation of phase transition waves, in that the temperature on the interface between the burned and unburned regions is constant, the combustion wave is described by a similarity solution which is a function of the similarity variable x/root t and the wave velocity decays as 1/root t.The difference between the two problems is that in the combustion problem the temperature is not prescribed, but rather, is determined as part of the solution. We will show that the length of samples in which such self-sustained combustion waves can occur, must exceed a critical value which strongly depends on the combustion temperature T-b Smaller values of T-b require longer sample lengths for diffusion driven combustion waves to exist. Because of their relatively small velocity, diffusion driven waves are considered to be relevant for the case of low heat losses, which occur for large diameter samples or in microgravity conditions. Another possible mechanism of porous medium combustion describes waves which propagate by consuming the oxidizer initially stored in the pores of the sample. This occurs for abnormally high pressure and gas density. In this case, uniformly propagating planar waves, which are kinetically controlled, can propagate. Diffusion of oxidizer decreases the wave velocity. In addition to the reaction and diffusion layers, the uniformly propagating wave structure includes a layer with a pressure gradient, where the gas motion is induced by the production or consumption of the gas in the reaction as well as by thermal expansion of the gas. The width of this zone determines the scale of the combustion wave in the porous medium.