Saudi Arabia steps in.

By launching direct military action against the Houthi/Saleh forces in Yemen the Saudis are taking a long term risk.  Though they might be by far the stronger party at the moment it is conceivable that they might meet strong resistance.  It is hard to subdue people who have nothing to lose and the Yemenis are very poor.  They also live in extremely difficult terrain.  Until now the Houthis were respecting the Saudi border.  Now that the Saudis have attacked them they will have no qualms about operating in Saudi territory.  Given there is significant Yemeni/Houthi population in the regions of Saudi Arabia which border Yemen's northern border, the Saudis are leaving themselves open to a war which could end up being fought on their own soil.  The Saudis may rationalise that if the Houthis gain complete control of Yemen they will, given past history, be after their southern regions next anyway.  This may be true, but the international community would have been virtually unified in opposing one country attacking another.  By Saudi Arabia attacking first they have forfeited this moral high ground.
The Saudis do already have the support, perhaps even the encouragement, of the United States of America in their attack and perhaps they believe that this is the only voice in the international court of public opinion that matters so why not invade.  This is a fair point, but America's priorities might change in the future while Yemen''s position on the southern border of Saudi Arabia will not and now that the Saudis have broken the peace I am sure the Houthis will be eager to take the fight into Saudi territory whenever they can.