This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The reduced models can then be directly obtained from a Galerkin projection to appropriately defined Krylov subspaces. The equivalence to a moment-matching procedure, previously implemented in , 2), is proved. A particular emphasis is placed on the reduction of the stochastic noise, which is absent in many order-reduction problems. In particular, for order less than six we can show the reduced model obtained from the subspace projection automatically satisfies the fluctuation-dissipation theorem. Details for the implementations, including a bi-orthogonalization procedure and the minimization of the number of matrix multiplications, will be discussed as well.There are multiple benefits from such an approach. For example, reduced models can capture directly the dynamics of certain quantities of interest. Secondly, with the reduction of the dimension, the computational cost can be reduced dramatically. In addition, the quantities of interest often correspond to slow variables. By eliminating fast variables, the time step can also be increased considerably. This allows one to access longer time scales ?.There has been tremendous recent progress in the development of coarse-grained models , 7, 9, 1, 3, 7,?, 5); , 0). Most effort, however, is thermodynamics based. Namely, one aims to construct the free energy associated with the reduced variables, which then yields the driving force for the reduced dynamics, known as the potential of mean forces (PMF) , 3, 4). As pointed out in , 3, 4), the damping mechanics, which also plays an important role in the reduced dynamics, is not part of the construction.In this work, we are interested in an equation-based derivation, where the reduced model can be derived directly from the Langevin dynamics. Deriving reduced models from a stochastic dynamical system has been a subject of extensive studies, the most well known of which is the homogenization approach , 9). Another important approach is to employ a coordinate transformation using normal forms to separate out the degrees of freedom that are less relevant , 3). More recently, Legoll and Lelievre proposed to use conditional expectations to derived reduced models , 5). Overall, these methods require either significant scale separation assumption, or simple functions forms in the stochastic differential equations, which for bi-molecular models, does not apply. For example, the force-field for biomolecular models typically involves complicated function forms.Meanwhile, in the field of molecular modeling there are also many methods that were proposed to coarse-grain a molecular dynamics model. Most of these methods are derived from a Hamiltonian system of ODEs ,9,1,7,8,4); ; ; , either motivated by or directly obtained, from the Mori-Zwanzig projection formalism , 5, 9). Strictly speaking, such a procedure...