We study a natural information dissemination problem for multiple mobile agents in a bounded Euclidean space. Agents are placed uniformly at random in the d-dimensional space {−n, ..., n} d at time zero, and one of the agents holds a piece of information to be disseminated. All the agents then perform independent random walks over the space, and the information is transmitted from one agent to another if the two agents are sufficiently close. We wish to bound the total time before all agents receive the information (with high probability). Our work extends Pettarin et al's work [13], which solved the problem for d ≤ 2. We present tight bounds up to polylogarithmic factors for the case d = 3. (While our results extend to higher dimensions, for space and readability considerations we provide only the case d = 3 here.) Our results show the behavior when d ≥ 3 is qualitatively different from the case d ≤ 2.In particular, as the ratio between the volume of the space and the number of agents varies, we show an interesting phase transition for three dimensions that does not occur in one or two dimensions. 0 1 each with probability 1/(2d). If an agent is at a boundary, so there is no edge in one or more directions, we treat each missing edge as a self-loop. Let Ξ 1 (t), ..., Ξ m (t) ∈ {0, 1} each be a random variable, where Ξ i (t) represents whether the agent a i is infected at time step t. We assume Ξ 1 (0) = 1 and Ξ i (0) = 0 for all i = 1. The value Ξ i (t) will change from 0 to 1 if at time t it is within distance 1 to another infected agent a j . (We use distance 1 instead of distance 0 to avoid parity issues.) Once a value Ξ j (t) becomes 1, it stays 1. Definition 1.1. (Information diffusion problem). Let A 1 , A 2 , . . . , A m ∈ V d be the initial positions of the agents a 1 , . . . , a m and let S 1 t (A 1 ), S 2 t (A 2 ), . . . , S m t (A m ) be m independent random walks starting at A 1 , . . . , A m respectively, so that S i t (P ) is the position of agent a i at time t given that at t = 0 its position was P ∈ V d . The infectious state of each agent at time step t is a binary random variable Ξ i (t) such that • Ξ 1 (0) = 1, Ξ i (0) = 0 for all other i, and