diff --git a/fftools/ffmpeg_sched.c b/fftools/ffmpeg_sched.c
index ed85bb16de..c5ee6971f1 100644
--- a/fftools/ffmpeg_sched.c
+++ b/fftools/ffmpeg_sched.c
@@ -1282,14 +1282,59 @@ int sch_mux_sub_heartbeat_add(Scheduler *sch, unsigned mux_idx, unsigned stream_
     return 0;
 }
 
+static void unchoke_for_stream(Scheduler *sch, SchedulerNode src);
+
+// Unchoke any filter graphs that are downstream of this node, to prevent it
+// from getting stuck trying to push data to a full queue
+static void unchoke_downstream(Scheduler *sch, SchedulerNode *dst)
+{
+    SchFilterGraph *fg;
+    SchDec *dec;
+    SchEnc *enc;
+    switch (dst->type) {
+    case SCH_NODE_TYPE_DEC:
+        dec = &sch->dec[dst->idx];
+        for (int i = 0; i < dec->nb_outputs; i++)
+            unchoke_downstream(sch, dec->outputs[i].dst);
+        break;
+    case SCH_NODE_TYPE_ENC:
+        enc = &sch->enc[dst->idx];
+        for (int i = 0; i < enc->nb_dst; i++)
+            unchoke_downstream(sch, &enc->dst[i]);
+        break;
+    case SCH_NODE_TYPE_MUX:
+        // muxers are never choked
+        break;
+    case SCH_NODE_TYPE_FILTER_IN:
+        fg = &sch->filters[dst->idx];
+        if (fg->best_input == fg->nb_inputs) {
+            fg->waiter.choked_next = 0;
+        } else {
+            // ensure that this filter graph is not stuck waiting for
+            // input from a different upstream demuxer
+            unchoke_for_stream(sch, fg->inputs[fg->best_input].src);
+        }
+        break;
+    default:
+        av_unreachable("Invalid destination node type?");
+        break;
+    }
+}
+
 static void unchoke_for_stream(Scheduler *sch, SchedulerNode src)
 {
     while (1) {
         SchFilterGraph *fg;
+        SchDemux *demux;
         switch (src.type) {
         case SCH_NODE_TYPE_DEMUX:
             // fed directly by a demuxer (i.e. not through a filtergraph)
-            sch->demux[src.idx].waiter.choked_next = 0;
+            demux = &sch->demux[src.idx];
+            if (demux->waiter.choked_next == 0)
+                return; // prevent infinite loop
+            demux->waiter.choked_next = 0;
+            for (int i = 0; i < demux->nb_streams; i++)
+                unchoke_downstream(sch, demux->streams[i].dst);
             return;
         case SCH_NODE_TYPE_DEC:
             src = sch->dec[src.idx].src;