By relying on a recent theory of transport in the mixed state and a related model of pinning in soft materials, the instantaneous critical current is introduced as a well-defined part I\ of the total constant current. This nondissipative and time-dependent I\ is assumed to be randomly distributed near the sample surface, and is described as a 2D turbulent homogeneous flow. Auto-and cross-correlation functions of both voltage and magnetic field noises are predicted and are in full agreement with experiments.PACS numbers: 74.60.Ge, 74.60Jg Flux-flow noise has been extensively studied, particularly during the 1960's and 1970's [1-6]. The spectrum and amplitude of the noise voltage dV(t), typically 10 ~^-10 "'' V/(Hz) ^/^ in the 0-10 kHz bandwidth, were regarded as significant parameters revealing the more or less irregular motion of vortex lines (VL) in the presence of pinning. The reader is referred to the excellent critical review by Clem [7]. In view of the experimental difficulties and the increasing intricacy of interpretations, this scope has been practically discarded since about 1980.It should be noted that soft samples were used, classically shaped as foils or strips perpendicular to the applied magnetic field. Low to moderate critical currents /^ are required to avoid spurious sources of noise due to excessive dissipation, such as flicker noise [7]. Therefore, at working temperatures (4.2 K [1,2,5] or close to the X point [6]), the authors had to operate at the onset of the /-K curve; in this region, where flux flow is essentially inhomogeneous along the sample [8], measurements yield unreliable results.Recently [9], we have reconsidered the problem of noise, both theoretically and experimentally. We have performed a series of experiments in superfluid helium in order to widely explore the flux-flow regime. Voltage noise, magnetic field noise around the sample, and thermal Joule noise [10] were investigated, as well as their cross correlations. By relying on a phenomenological theory of vortex motion, recently published by two of us, Mathieu and Simon (MS) [11], we were able to work out a consistent theory of noise, the principle of which is brought forward in this Letter.Roughly speaking, two mechanisms have been advanced to account for the voltage noise quantitatively. In their pioneering work, van Ooijen and van Gurp [1] assumed that flux bundles nucleated randomly at one edge and moved rigidly across the sample with constant velocity VL. This process gives rise to a time sequence of statistically independent pulses, the cutoff' frequency of the noise spectrum being related to the time of flight of bundles. This analogy with the electronic "shot noise" was attractive, but more and more adjustable parameters were introduced to fit the data; besides the flux bundle size ipb, others include the fraction of pinned vortices [2], or a distribution of subpulse times [6]. Somewhat artificially, ipb is found to be a rapidly decreasing function of current, falling off* below the flux quantum <^o [2,6]. Moreov...