diff --git a/ggml/src/ggml-cpu/ggml-cpu.c b/ggml/src/ggml-cpu/ggml-cpu.c
index 24c47569c..8620c6c7a 100644
--- a/ggml/src/ggml-cpu/ggml-cpu.c
+++ b/ggml/src/ggml-cpu/ggml-cpu.c
@@ -1334,9 +1334,11 @@ UseGgmlGemm1:;
         const size_t nbw3 = nbw2*ne12;
 
         assert(params->wsize >= ne13*nbw3);
-        GGML_ASSERT(src1->type == GGML_TYPE_F32 || src1->type == GGML_TYPE_F16);
-        // the F16 path below writes plain floats into wdata, so it needs an F32 vec_dot_type
-        GGML_ASSERT(src1->type == GGML_TYPE_F32 || vec_dot_type == GGML_TYPE_F32);
+        // src1 is either packed from F32 into vec_dot_type, or widened from F16 or BF16 into the F32 work buffer
+        const bool widen = src1->type != GGML_TYPE_F32;
+
+        GGML_ASSERT(!widen || vec_dot_type == GGML_TYPE_F32);
+        GGML_ASSERT(!widen || src1->type == GGML_TYPE_F16 || src1->type == GGML_TYPE_BF16);
 
     #if 0
         for (int64_t i13 = 0; i13 < ne13; ++i13) {
@@ -1349,20 +1351,24 @@ UseGgmlGemm1:;
             }
         }
     #else
+        const int64_t bs = ggml_blck_size(vec_dot_type);
+
         for (int64_t i13 = 0; i13 < ne13; ++i13) {
             for (int64_t i12 = 0; i12 < ne12; ++i12) {
                 for (int64_t i11 = 0; i11 < ne11; ++i11) {
-                    size_t bs = ggml_blck_size(vec_dot_type);
                     int64_t ne10_block_start = (ith * ne10/bs) / nth;
                     int64_t ne10_block_end   = ((ith + 1) * ne10/bs) / nth;
-                    const char * src1_block = (const char *) src1->data + i13*nb13 + i12*nb12 + i11*nb11 + ne10_block_start*bs*nb10;
-                    char * dst_block = wdata + i13*nbw3 + i12*nbw2 + i11*nbw1 + ne10_block_start*nbw0;
-                    const int64_t n_block = (ne10_block_end - ne10_block_start) * bs;
+                    const void * src1_row  = (const char *) src1->data + i13*nb13 + i12*nb12 + i11*nb11 + ne10_block_start*bs*nb10;
+                    void       * wdata_row =                    wdata  + i13*nbw3 + i12*nbw2 + i11*nbw1 + ne10_block_start*nbw0;
 
-                    if (src1->type == GGML_TYPE_F32) {
-                        from_float((const float *) src1_block, dst_block, n_block);
+                    const int64_t ne10_block_size = (ne10_block_end - ne10_block_start) * bs;
+
+                    if (src1->type == GGML_TYPE_F16) {
+                        ggml_cpu_fp16_to_fp32((const ggml_fp16_t *) src1_row, (float *) wdata_row, ne10_block_size);
+                    } else if (src1->type == GGML_TYPE_BF16) {
+                        ggml_cpu_bf16_to_fp32((const ggml_bf16_t *) src1_row, (float *) wdata_row, ne10_block_size);
                     } else {
-                        ggml_cpu_fp16_to_fp32((const ggml_fp16_t *) src1_block, (float *) dst_block, n_block);
+                        from_float((const float *) src1_row, wdata_row, ne10_block_size);
                     }
                 }
             }
diff --git a/ggml/src/ggml-cpu/ggml-cpu.cpp b/ggml/src/ggml-cpu/ggml-cpu.cpp
index 1df0f2bb9..81ff5d79f 100644
--- a/ggml/src/ggml-cpu/ggml-cpu.cpp
+++ b/ggml/src/ggml-cpu/ggml-cpu.cpp
@@ -455,7 +455,10 @@ static bool ggml_backend_cpu_device_supports_op(ggml_backend_dev_t dev, const st
                 src0->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32) {
                 return src1->type == GGML_TYPE_F32 || src1->type == GGML_TYPE_F16;
             }
-            return src1->type == GGML_TYPE_F32 || src1->type == ggml_get_type_traits_cpu(src0->type)->vec_dot_type;
+            // BF16 in src1 is widened into the F32 work buffer
+            return src1->type == GGML_TYPE_F32 ||
+                   src1->type == ggml_get_type_traits_cpu(src0->type)->vec_dot_type ||
+                   (src1->type == GGML_TYPE_BF16 && ggml_get_type_traits_cpu(src0->type)->vec_dot_type == GGML_TYPE_F32);
         case GGML_OP_SOFT_MAX_BACK: {
             if (op->src[0]->type != GGML_TYPE_F32 || op->src[1]->type != GGML_TYPE_F32) {
                 return false;
diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index e23d5b433..cbd3697ef 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -15441,6 +15441,10 @@ static bool ggml_backend_vk_device_supports_op(ggml_backend_dev_t dev, const ggm
                     // So don't support this combination for now.
                     return false;
                 }
+                if (op->src[1]->type == GGML_TYPE_BF16 && op->src[0]->type != GGML_TYPE_BF16) {
+                    // BF16 in src1 is only served by the BF16 x BF16 pipelines
+                    return false;
+                }
 
                 return true;
             }